What are the rules around closing Catholic churches that are part of restructured parishes?
The bishop with the diocesan presbyteral council may make the decision in this matter. At least Canon Law accords them the power to do so. It sucks, but that is what it is.
Can. 1222 §1. If a church cannot be used in any way for divine worship and there is no possibility of repairing it, the diocesan bishop can relegate it to profane but not sordid use.
§2. Where other grave causes suggest that a church no longer be used for divine worship, the diocesan bishop, after having heard the presbyteral council, can relegate it to profane but not sordid use, with the consent of those who legitimately claim rights for themselves in the church and provided that the good of souls suffers no detriment thereby.
Financial impossibility of maintaining a parish church constitutes a ”grave reason” for selling a local parish church! See the following article: Canon Law and Selling a Church
In restructuring the diocese, the parish in question no longer exists!