How to deal with a aging parent who is shoplifting?

If you take someone with a shoplifting habit to stores, sooner or later the police will be involved. So option A is to let the legal system deal with her problem, which may involved a 72 hour inpatient psych evaluation.
Option B depends on whether or not you are legally responsible, such as a POA or Guardian, who takes her shopping. In this case the court may find you negligent and order you make restitution to the complainant.
Option C is the simplest, just don't take her to stores, period.

There are some things about the psychology of shoplifting online. They looked interesting.

Or give her a list of things you need. :D

Oh, I'm sorry. I'm so evil. The problems underlying shoplifting are often deep. For example, we had a commanding officer at Ft Benning whose wife was a chronic shoplifter. They could have easily afforded the things she took, but she took things, anyway. I am not a psychologist, so I don't understand the need and compulsion to steal. You may want to address that psychological problem or just leave her at home.

Is she developing dementia? Try contacting the stores she frequents to let them know what is going on by taking the items stolen to the store and pay for them. You would not want to be charged as an accessory. Ask them to deal with her whenever this happens and if they are told, life will be easier for her.

Or just do not take her shopping. If you do, you know you have to keep a close eye on her. Do not let her take the purse or anything else into the store where she can hide things.