In this case the bishop closed two churches (small “c”) but at least one of the parishes still exists. (I don’t know why the church buildings were closed. Maybe the property had to be sold to pay off debts and a new larger building will be built in a less expensive area?
In any case, “new” parishes or existing parishes who lose the use of a building have to hold Mass in some other facility while waiting for a new building. Unless there is a large Catholic college chapel nearby that usually means Mass in an auditorium, gym, industrial building, or the like. Sometimes a nearby protestant parish will offer it’s building because it has fewer Sunday services and the building is already setup for worshiping.
I know of at least one case in Arizona where a brand new Catholic parish “moved in” with an existing Lutheran parish while the Catholic parish raised money and eventually built a church. Once the Catholic church was being used, the parish loaned out it’s hall to a Lutheran parish that had been newly formed.
Usually the “visiting” congregation pays a fee for the use of the building (utilities, maintenance, etc.)