Can a closed but undischarged mortgage be reopened easily?

As you asked about other countries:

In Germany, if your bank as a mortgage on your house, it can be used as a security for other loans as well.

Assume your house's value is 150000 €, and after several decades, you have managed to pay off 130000 €, it is very possible that, if you need a loan, be it for repairs or for ther purposes, you can get a loan secured by the house.

If one (for whatever reason) happens to have an existing mortgage that has been fully paid off but never officially discharged, can that mortgage be easily reopened to get a new loan without having to go through the original application process all over again?

In the united States the lender would have to reevaluate your financial situation, and make sure that there is no liens on the house.

Some lenders while you have a mortgage with them can quickly approve a refinancing of the mortgage. But they would be hesitant to do so if there was a break.

They need to know that you currently have the income to payoff the new loan; they need to know that your other debts aren't too big; they also need to know that your credit history hasn't gotten worse. They will still need an appraisal of the collateral and a title search and maybe even a new title insurance policy.

I doubt it would save a lot of time.