In some cases you have a lineup that's complete, so those considerations are academic. As they set out touring behind their nineteenth studio album, Los Lobos have their core membership intact, though one wonders if they'd still be a viable operation if they were to lose David Hidalgo and/or Cesar Rosas.
I've remarked elsewhere there's a body of opinion that it can't be Little Feat without Lowell George, or the Allman Brothers Band without Dickey Betts, and I guess this is the place to look at those factors more closely.
Each case, of course, needs to be considered on its own, and there's no way you can come up with a hard and fast rule. In many cases the lack of a high profile iconic figure means that you can get by without a single surviving member of the classic line up. If you see The Drifters, for example (and I have, that's why I use the example) you're not going to be expecting to see Ben E. King out front and provided you hear what you expect to hear and it sounds the way it's supposed to sound you'll probably go away happy.
With Little Feat, on the other hand, things are slightly more complicated, particularly now that Richie Hayward has gone to join Lowell George at that great gig in the sky. For a start I should point out that there were two Lowell-era lineups, and that the reformed outfit that has been touring and recording since 1988 has been remarkably stable, and reasonably prolific in terms of new material.
Given the fact that most people are unaware of the band's existence (at least in these parts, I'd like a dollar for every Who? that's come back at me when I refer to one of my all-time favourite bands) and if they are they probably don't differentiate between the quartet that produced Little Feat and Sailin' Shoes and the six-piece outfit that produced Dixie Chicken, Feats Don't Fail Me Now, The Last Record Album and the live Waiting For Columbus.
If you're familiar with those albums, you'll probably have your own opinion on The Lowell George Question, but you'd also possibly be aware that Lowell was encouraging greater contributions from his band mates, particularly Bill Payne and Paul Barrere. He didn't always like the results, but he was looking for someone to share the load.