"Compressor shut" is a bit vague - what exactly did he say was wrong with it? These units usually use scroll compressors these days that are impossible to open for repair in the field but they could be repaired in a well stocked, specialized shop. If by "repair" you mean "replacement with same or OEM replacement compressor" then yes, it can be done by a qualified technician.
Replacing a compressor is a very large undertaking and I would first find out more about what exactly was found wrong with it. If it does not even come on, then it's often the external electrical parts that fail (relays, capacitors) and those can be relatively easily replaced, although you still need a qualified tech or a DIYer very confident with high voltage electrics to do it
Repair man come out yesterday, first told her it was out of freeon, then upon testing for leak discovered the compressor was out, can the compressor be repaired, or does it need to be replaced, they are on a fixed income, so not a lot to work with and a new system is out of the question.
The compressor can be replaced, however, a unit that old is not worth the investment which depending on the btu rating could be well over $1,500.00. I don't understand why the tech would say the unit was low on refrigerant 1st. He shoul have found the defective compressor 1st because it is impossible to see a low charge without the compressor running. I would suggest you invest in another HVAC contractor to recheck the unit. If the compressor is bad they can tell, but it could be an electrical problem or a defective capacitor or relay.