The most awkward examples of the show going on...

[TMC]

For example:

• 8 Simple Rules shambling on after John Ritter died.
  
• Another John Ritter example, There's Company when Suzanne Somers was trying to renegotiate her contract.
  
• Two and a Half Men going on despite publicly losing one and a half of the men.
  
• The last season of Chappelle's Show.
  
• This is kind of debatable, but continuing with The Conners after Roseanne Barr was fired had her moment.
  
• The Office after Steve Carrell left.

[biffbronson]

Laverne & Shirley, continuing as such after Shirley was no longer on the series?

[Merry24]

Fuller House going without the Olsens

Saved By The Bell Reboot without Dustin Diamond when he was alive

Three’s A Crowd without Joyce Dewitt

Dennis the Menace without Joesph Kearns

Modern Family because they wanted to go 10 Seasons

The Goldbergs because abc was trying to make a point to Jeff Garlin.

Andy Griffith Show without Don Knotts.

Archie Bunkers Place without Jean Stapleton & Sally Struthers

Even though it came out good but Susan Olsen & Allen Melvin not in A Very Brady Christmas

[TMC]

• NewsRadio after Phil Hartman was murdered. Even though he wasn't really playing the main character (Dave Foley was), he was none the less, arguably still the glue that held the show together. While Jon Lovitz tried his best in that final season, you could that tell no one's heart is in it anymore.
  
• The last season or two of Grace Under Fire. Brett Butler was becoming increasing difficult to deal with due to her substance abuse issues and overall, prima donna behavior. By the last season, it was apparent that they waiting until they could get to the "magic number" of 100 episodes (so that it would look better for syndication) before calling it a day.
  
• Just about any time that a show recasts a major character like of course, the infamous Darren Stephens switch (Dick York being replaced by Dick Sargent) on Bewitched.

[TMC]

Originally Posted by biffbronson

Laverne & Shirley, continuing as such after Shirley was no longer on the series?

I can't believe that didn't come to my mind, but yes. It made no sense to keep calling the show Laverne and Shirley after Cindy Williams (RIP) was officially out of the picture. That last season was utterly tragic. You know that the show was over upon seeing the opening with a now solo Penny Marshall watching a group of school kids do Laverne and Shirley's "Schlemiel and Schlimazel":

[TMC]

Originally Posted by Merry24

Fuller House going without the Olsens

Saved By The Bell Reboot without Dustin Diamond when he was alive

Three’s A Crowd without Joyce Dewitt

Dennis the Menace without Joesph Kearns

Modern Family because they wanted to go 10 Seasons

The Goldbergs because abc was trying to make a point to Jeff Garlin.

Andy Griffith Show without Don Knotts.

Archie Bunkers Place without Jean Stapleton & Sally Struthers

Even though it came out good but Susan Olsen & Allen Melvin not in A Very Brady Christmas

• Chico and the Man trying to continue after Freddie Prinze's suicide.
  
• Sanford and Son when Redd Foxx went on his strike and they had Grady (Whitman Mayo) essentially fill-in.

[Merry24]

Yes, Laverne without Shirley was a wow! I remember they had to redo that last season opening again slightly because Michael Mckeenen AKA Lenny also left. It was ..

Carmine
Frank without Mrs.Babbish
Squiggy without Lenny
Laverne without Shirley

[TMC]

So Random, which was the All That-esque show within a show on Sonny With a Chance becoming defictionalized after the star of the show (and the proverbial "Sonny"), Demi Lovato abruptly left the series after its second season. So it went from being a sitcom about the behind the scenes shenanigans of sketch comedy show (kind of a 30 Rock for kids) to a full-blown sketch comedy show (like I said, in essence Disney Channel's version of All That) with the remaining Sonny With a Chance cast members.

[TMC]

Originally Posted by Merry24

Fuller House going without the Olsens

Saved By The Bell Reboot without Dustin Diamond when he was alive

Three’s A Crowd without Joyce Dewitt

Dennis the Menace without Joesph Kearns

Modern Family because they wanted to go 10 Seasons

The Goldbergs because abc was trying to make a point to Jeff Garlin.

Andy Griffith Show without Don Knotts.

Archie Bunkers Place without Jean Stapleton & Sally Struthers

Even though it came out good but Susan Olsen & Allen Melvin not in A Very Brady Christmas

Since Saved by the Bell was mentioned, how about that weird season where Leanna Creel joined the cast as Tori? The series finale, where the gang graduated from Bayside High had already been shot. But NBC decided that they wanted additional episodes to help pad its run. However, Tiffani-Amber Thiessen (Kelly) and Elizabeth Berkley (Jessie) were conspicuously absent from these new episodes. I assume that it's because the cast's contracts had to be renegotiated and Thiessen and Berkley couldn't be bothered. In those episodes with Tori, they all but act like Kelly and Jessie never existed. Even so, if I'm not mistaken, NBC aired two episodes of Saved by the Bell on Saturday mornings, one with Kelly and Jessie and another with Tori.

[howilu]

I would cast my vote for Chico and the Man after Freddie Prinze shot himself in the head. It wasn't good with Jack Albertson as a solo show and worse with Gabriel Melgar. Much of the humor was lost with Prinze's passing. The exchanges between Ed and Chico were the high point of the show.

[merlinjones]

Valerie without Valerie Harper (aka The Hogans, The Hogan Family)
Rosanne without Rosanne Barr (aka The Connors)
Petticoat Junction without Bea Benederet
Bewitched without Dick York
The Lucy Show without Viv
The Doris Day Show without anyone from season one but Doris
Sanford and Son without Redd Fox
Good Times without Esther Rolle and John Amos
Alias Smith and Jones without Pete Duel
The Waltons without John Boy, Mama and Papa
Hawaii Five-O without Dan-O
Walt Disney's Wonderful World of Color without Walt
77 Sunset Strip without Kookie and Jeff

[icecream]

Originally Posted by merlinjones

The Waltons without John Boy, Mama and Papa

The Waltons wasn't totally without John-Boy. They recast him which was worse.

[merlinjones]

My Three Sons without any of the original sons (Mike, Robbie or Chip)

Mayberry RFD in general

[Merry24]

Little House On The Prairie-Melissa Sue Anderson was written out.

Little House A New Beginning-The entire core cast gone except Melissa Gilbert.

Little House All The Dear Children & Little House The Final Farewell. Should have brought Katherine Mcgregor & Alison Arngrim and Melissa Sue Anderson and Lindsay or Sydney Greenbush back and maybe even Charlotte Stewart as well.

[TMC]

• The Dukes of Hazzard during that one season where they had Coy and Vance take over from Bo and Luke when the latter sat out for that season over a pay dispute.
  
• The final season of Martin, when Martin Lawrence couldn't be filmed in the same place and time as Tisha Campbell, after the latter accused Lawrence of inappropriate conduct on set. This was extremely problematic to work around because their characters were married to one another.
  
• After Valerie Harper was abruptly dismissed from the sitcom with her namesake, Valerie, the show initially went on with the title Valerie's Family, before finally settling on The Hogan Family.