I've been in similar situations.
Situation 1: I had an offer to join YCombinator company. I got the offer shortly after they were accepted to YCominator, but before they had a product, customers, or any other funding. I negotiated the offer to ~23% of the company (which was an equal share as the founders) and zero salary (not even living expenses).
Situation 2: I had an offer to join a brand new company founded by veteran, very successful entrepreneurs. They had $450k in funding, but no product or customers. I negotiated the package to 60% market salary plus 4% equity share.
Receiving subsistence wages and zero equity should be completely unacceptable. If they have no product and no customers, then the starting point for negotiations should be co-founder status - 30% equity share (with normal vesting of course). Don't be afraid to be a tough negotiator, just argue in good faith and back your arguments with reason.
Startups are usually a great learning experience. But they demand enormous amounts of work and stress. Life is short, and you only have so many shots. Thus with each startup you undertake, you must maximize the chance that it can be the hit that changes your life. Joining a startup without taking a share in the upside is completely insane.
Finally, you have to settle this ASAP, not at the end of the summer. If the company continues to exist, the shares will rise in price. If you wait until later to negotiate stock, the equity will be more valuable, and you'll get less of a share than you would at the moment. Thus by working now but negotiating later, you'll be assuming all the risks of joining a startup at the beginning, but only getting equity based on a later valuation that assumes less risk. That's a raw deal for you.
