There were some financial repercussions which I recovered from quickly. The lasting issues were from burnout as a result of working myself to death trying to deliver (and likely exacerbated by pre-existing depression issues).
I'm actually not sure whether it would cause employment issues because I haven't had any desire to program professionally since then (it was a couple years ago).
I was the last engineer of a small startup (from 4 full-time employees + ~4 contractors). I stayed a year beyond everyone except the founder/CEO in an attempt to launch the nearly-ready service, despite clear red flags. I achieved the established technical goals multiple times, but it became obvious the product would never launch due to non-technical reasons. It was a big mistake from which I have not completely recovered.
I'd suggest seriously considering what you hope to achieve and what you can reasonably expect from several angles: Financial outcomes, career trajectory, and personal motivations to name a few.
A few relevant questions: Have the issues which led to the current stagnation been addressed? Does the startup have a product that has been validated and can produce sustainable revenue? If not, what is the likelihood of securing (more) funding? Are you being paid well (without considering any equity/options)? How will your decision to stay look to future employers, considering likely outcomes? Why do you want to stay? Because you enjoy it? The challenge? Responsibility/Obligation (and to whom)? Sunk costs? Ego? Hubris? Messiah complex?
If you do decide to stay, I would suggest setting concrete limits/criteria for when to move on, so you don't get stuck in a zombie company.
I'm actually not sure whether it would cause employment issues because I haven't had any desire to program professionally since then (it was a couple years ago).