A bank acts according to the rules that are in force for the fixed deposits made with it.
Other financial institutions follow their own rules and they are not similar to that of the bank.
In case of a matured fixed deposit not claimed by an individual the institution would send the money back to the investor.
There might be cases where maturity instructions are taken from the investor at the time of making the deposit.
The company or institution might also hold the money while the investor makes the claim to the matured fixed deposit.