This needs to be negotiated with the lender.
Consider this: you get one 10000 USD loan with 200 USD monthly payment and another 40000 USD loan with 800 USD monthly payment with equal lengths. Then if you pay 10000 USD for the 10000 USD loan, obviously it will vanish so your monthly payments do really get reduced by 200 USD.
However, if you have only one 50000 USD loan, and suddenly have 10000 USD you want to use to reduce the loan, any of these could be true:
- Loan length will be reduced with monthly payments being the same
- Monthly payment will be reduced with loan length being the same
Do note that you always have option for refinancing your loan. So, if you suddenly have 10000 USD, you can take a new 40000 USD loan with different terms and use the 40000 USD + 10000 USD to pay back your 50000 USD loan. So, if you really want to reduce your monthly payment instead of loan length and the bank won't agree, you can explain this option of refinancing the loan to the bank. I'm sure they will agree later.
And one more important thing to remember. Loans with a fixed or long interest rate can't always be paid back without extra penalties!
The important think from bank's perspective about fixed or long rate loans is that they invested 50000 USD into a financial instrument that yields let's say 4%. If that's a 10-year bullet loan (assuming for simplicity), they will have 1.04^10 * 50000 = 74012.21 USD at the end of the loan period. Now if the market rates reduce to 2%, of course you want to take a new loan with 2% rate to pay back the old loan with it. If you do that, the bank would have only 1.02^10*50000 = 60949.72 USD. The bank just lost 13062.49 USD.
The only way to stop reducing interest rates from acting as a one-way clutch to reduce the bank's profit is to forbid paying back fixed/long-rate loans in conditions where the market rates are reduced, unless you pay also what the bank loses in the process of paying back the loan.