Can a rattle can that's half full of paint, but from which all of the propellant has leaked out, be used for anything other than a paperweight?
For example, can the paint be extracted and used in some kind of craft or upcycling project that specifically needs paint formulated for a spray can?
Repressurize
You can repressurize the can. If you have a compressor, a valve stem from a tire makes a good adapter (insert the service end into a tire filling adapter, and use the rubber end that goes inside a tire to make a seal on the spray can). You put it over the "stem" that the nozzle fits on, press down to make a seal on the can, and fill to around 70 PSI. Here's a video showing the process: HOW TO REPRESSURIZE SPRAY CANS.
You can also do it with a butane lighter refill canister (butane is often what is used as the propellent). You just use the refill canister to pressurize the can through the stem the same way a butane lighter or hobby torch would be refilled. Here's a video showing that process: Repressurize spray cans with lighter refill.
Quick discussion on pressure. You need enough pressure to push the paint out properly, but more isn't better. Too much pressure and the spray quality will be affected. Compressed air isn't what's used when the cans are filled at the factory. The propellant is something that's a gas at room temperature but a liquid under pressure. As you spray and use up the paint in the can, more propellant evaporates inside the can to maintain the pressure. The pressure in the can is determined by the vapor pressure of the propellant, so it stays constant as long as there is propellant in the can.
Compressed air doesn't liquefy at a temperature or pressure useful for spray cans. It remains a compressed gas, and the pressure goes down as it expands to fill the space in the can when you spray. With compressed air, you need to put in a little more pressure than needed so that the pressure doesn't drop too low as soon as you spray a little. But you don't want so much pressure that the paint doesn't spray correctly.
Typically, if you run out of original propellant, there isn't much paint left in the can. So one filling with compressed air will let you use up the contents. If you manage to empty the propellant on an almost full can (like by spraying with the can upside down), you might need to do several fills with compressed air to keep the pressure in a good range for spraying.
You won't be able to overpressurize with a butane refill because butane vapor pressure isn't that high. With an air compressor, around 70 psi is optimal (it's a little more than what's needed). If you exceed around 90 psi, it may affect the quality of the spray.
Safety
As a safety matter, you won't run into problems if you stay in that range. Can strength needs to meet certain minimums regulated by the government. In North America, the lowest grade spray can must pass pressure testing at 140 psi without deforming or buckling, and 210 psi is the minimum burst pressure. South American standards are very close to that. In Europe and many of the Asian countries, the minimums are higher. So if you go nuts with an air compressor, you will get feedback, like the can starting to balloon well before it bursts.
As far as hazards, it always makes sense to use eye protection, and it doesn't hurt to protect your clothing. You're working with paint and pressure, so take common sense precautions because mishaps can always happen. Butane isn't toxic, and there isn't enough of it in a refill canister to be unusually dangerous when used properly. But it's flammable, so don't repressurize with butane around an ignition source.
In a comment, A.K. asked about toxicity and the need for a respirator. Any toxicity would be in the paint, and most people using spray paint cans would wear a respirator only if they were doing a lot of spraying in an enclosed space. Unless you plan to seriously over-pressurize the can to the point of bursting, there wouldn't be a need for a respirator.
Extract the remaining paint
If you don't want to repressurize, you can empty and save the contents into a suitable container. Make sure there is no pressure in the can. Then drill a small vent hole near the top with the can upright to vent any remaining pressure. On the opposite side near the top, drill a drain hole. Then pour the contents into the container.
@StuartF makes a great point in a comment. The can may not have enough propellant to push out the contents, but it could still have some pressure. Wear protective gear for you and your clothes when you make the vent hole. The suggestion of puncturing the can by pushing it away from you into a fixed point is a good idea.
Repurposing the can
With the can empty, you could add something like sand if you really want a paperweight. :-) Or after the inside has dried out, use it as a cylindrical form for something crafty.
