Reusing an existing foundation is no different than designing a new foundation. Bending, shear, soil bearing pressure, and bar development all need to be checked.
We do a fair amount of this kind of work, and I concur with DaveAtkins. Baring any exceptional past loading conditions or unsusual events which would cast severe doubt on the structural integrity of the foundation the following should answer any potential concern:
1. conduct a new soil investigation to verify the soil parameters and consequently the integrity of the initial design of the footing vis-a-vis the expected future loads. This would answer the question of footing's dimension and soil bearing capacity, and in case of loads over and above what the footing had been exposed to, you'll be able to determine any potential additional settlement.
2. If the footing is not exposed, expose several footings under the building's footprint (center, corner, sides) in order verify the as-built against actual footings dimensions.
3. Collect few cores from the exposed footing and complement that with a bunch of Shmidt hammer tests. This would provide you with an overall idea about the existing concrete strengths (and integrity) as well as a verification of the footings' dimensions. You might want to complement that with a scanner survey to determine/ verify the steel reinforcement withing the footing.
4. With these data you can go back to your desk and verify the moments, shear, settelment etc... will pass.