As a preliminary note, a good solution to this problem will (as usual) involve talking to your players. Ask them if they think this is even a problem, and if so, what kind. You may find that they enjoy being reckless and don't mind dealing with the consequences, even if that means inaction or even death for their characters. If so, congratulations: you're all set! But if they don't want to be unconscious and bored, read on.
You can try different things to keep them entertained, like having them run NPCs, narrate the combat to make it more epic, or take notes for posterity. If your players are flexible, that may work, and they may even enjoy the change of pace. (Though honestly, in my experience once they're stabilized it's usually a good time for a bio break to get more drinks for everyone or take care of other necessities, which should resolve the situation nicely unless it's a really long fight.)
However, most players are at the table because they want to play their characters. (Not all of them, but most of the standard motivations require being able to influence the game in some capacity, and most of those involve investment in a specific character.) If that's true, then no substitute will ultimately be as satisfying as being in there with your own character, mixing it up.
So if I could back up a bit, I would ask a different question, namely, why is this situation occurring so frequently that you have to ask?
If PC's routinely get KO'd, I suspect one of three things is true: A) your PC's are low level; B) your PC's are employing bad strategies; or C) your encounters are structured in a way that causes a lot of KO's, possibly because you're using Glass Cannons (warning: TVTropes).
A) should resolve itself pretty quickly. B) might resolve itself as your players learn better strategies, but you may need to ask if they want any pointers. If it's C), though, you can fix this by adjusting your tactics, both in building encounters and how you run them. A plan failing because "You didn't even dent her armor!" can be as spooky as one failing because they spotted you and stabbed you. (Of course, if you go too far with defensive enemies, fights can drag on forever, but sometimes people have to be defeated in a particular way that requires a little in-game research or experimentation.)
More importantly: if your boss fights are deadly and/or you've successfully cultivated an atmosphere where they feel deadly, when a PC does drop your players should be scrambling to get them back up so they don't lose the advantage of numbers (not to mention, y'know, keeping them alive). You've said the party doesn't have a ton of healing, but you can influence that by pointing them towards Goodberry and other useful spells and abilities, adding an NPC, or just giving out healing potions as loot (something that's working pretty well for 2 groups I'm in with relatively little healing). If people are watching each other's backs, a PC shouldn't be down for more than a round or so.
If you take the above into consideration, I think you can probably settle into a rhythm where this isn't too much of a problem in the first place.