How can I prevent my bicycle chain from slipping off the sprocket?

Maybe take it to a local bike shop with some coffee and see if they’ll shorten your chain for the coffee?

If the spacing between the wheels is stable, then the chain is somehow lengthening, apparently (unless you have even more serious wear issues of the sprockets themselves, which seems unlikely to me). And for a bicycle chain to be continually lengthening indicates that it is nearing the end of its life.

I’d look into replacing the chain, if I were you.

The tool to remove a link is cheaper than a new chain- plus, when you get a new chain, you usually need new sprockets as well, as the chain wears with the sprockets.

Is this a single-speed or a geared bike? If it has gears, you may need to adjust your derailleurs.

If the chain is that long and still meshes with the gears, then the gears are also toast, so I would not recommend changing the chain unless you also replace the gears at the same time. Otherwise, bad things will happen, and by “bad”, I mean, the sort of thing that will make you wonder why you spent money to have worse problems than the one you were originally trying to fix.

Removing a link is a simple job involving an inexpensive tool. Or a friendly neighborhood bike shop could remove a link in less than two minutes. It will also keep the chain and gears matched up enough to avoid problems… until the chain snaps, and then you will be shit out of luck.

Sounds like you have a single speed bike, although advice for a multi-speed bike is similar. If you can’t pull the rear wheel backwards any further in the dropout to tighten the chain then you should either replace the chain (often this will necessitate replacing the rear cog too) or shorten the chain by removing a link. You will need a chain tool for the latter, any decent repair shop can sell you the tool or handle the former.

What @jerv said. If you let a chain get too worn, it starts to wear out the sprockets, too. You can get a new chain (and a little Rivoli rivet tool to fix it yourself) and see if that helps, but it will still skip on you if the sprockets are appreciably worn. It sounds like you’re riding a single-speed bike? You’d probably need to get that fixed at a shop.

@IchtheosaurusRex I had one bike where the sprockets were so worn that a new chain would not fit. That forced me to remove three links before my derailleur could take up enough slack to use all of my gears.
The nice thing about being poor or frugal is that you wind up with all sorts of repair skills ;)