Is it possible to flag a delinquent account?

In the Family record, on the Summary tab, you can designate a family as a "Problem Account" and specify the reason in the Notes field on the Misc. tab. 

When set to yes, the Problem Account label turns red, and within Global Search, this account row is colored red. This can be used to help your staff be aware of a problem and where to read more about the issue (Family record > Misc. tab > Notes field).

Parent Portal - Block Registration for Problem Accounts

This can also be used to block the family from registering in additional classes in their Parent Portal (see  Tools > Parent Portal > Settings > Class Enrollment Settings > Prevent Problem Families from enrolling).