The option seller needs to buy the stock to deliver the shares when the option expires, so if the price continues rising their losses are unbounded (by contrast, their gains are bounded by how much they originally sold the option for).
Not just when the option expires. You can be assigned anytime after you sell an option.
Correct me if wrong, but my understanding with Robinhood is that you Sell to Close (by default anyway), which just goes back into the market. No further obligation?
If you sell an option, you Sell to Open. If you want to buy it back (at a profit/loss and you're not assigned), you Buy to Close which goes back into the market and closes your position. If you are assigned (i.e. the buyer of your option exercises his right to buy 100 shares at the strike price), you have no option other than to buy those shares at market price if you don't have any and deliver it to the option buyer.