There is a frozen user that is eligible for clearing now and s/he has a pet name that I'd like to acquire -- When her account gets cleared, will his/her pets also be cleared?

Yup! C:

/kind of wish I had more to add than that, but oh well

Unless it was a self-freeze and the user in question unfreezes before the next clearing that should be the case, yes. During clearings accounts are deleted completely what also will free the pet names that sat on them.

Thank-you guys so much ;o