"If a business cannot sustain itself, it has gone bankrupt" might work for some more traditional cash-flow businesses, but I don't think that it applies very well to startups.
Very few investors will see it as a good sign if the founders pay themselves at or above their market rates, or if they do at or below the market amount of work. Likewise, the competition will punish startups for slacking or blowing money too fast.
It really is as simple as that.
*Based on studies I've seen and hundreds of people I've talked to across these industries. Bankruptcy is a legal process that you have to initiate and won't happen if you refuse to initiate it.
And whether those investors wanted anything in return or not, doesn't matter. Said founder/writer/actor/bandmember/mathematician still could not do their work if somebody hadn't put food on the table.
You really do have to stay alive and relatively healthy, if you want any chance at success.
Do you mean contemporary tech startups? As you may know, startups are businesses after all and the rules governing their operations are the same. When your business runs out of cash , you need someone to throw you a lifeline (debt or equity), or sell some assets to raise money or unfortunately file for bankruptcy and let nature take its course and creditors to recoup some of their investments.