What Frank said. Oil wells almost never "dry up", but there are a lot of expenses involved in keeping one pumping; taxes, regulatory compliance, the cost of electricity (to run the pump), chemicals, transportation of the oil, royalties, office overhead, the pumper (guy to check on it every day), repairs to the tubing and sucker rods, etc., etc. It is usually just a matter of simple economics when you quit pumping a stripper well. When it costs you more to operate it then you get after paying all of those bills, then you plug it. If the well is in a water-drive reservoir, then it could suddenly produce all water instead of oil, but that is still just economics.
If an older stripper well was plugged and abandoned, it is probably not worth the money to re-enter it and drill out the plugs and re-perforate it, but if it was just shut-in and not plugged then it could be returned to production fairly easily as long as the casing, tubing, and pump are still there and in good shape. The state will usually require the operator to plug and abandon the well if it has not produced in a certain amount of time.
As has already been said, the oil business is very risky and requires a lot of capital (money).