DEFINITELY NOT.
Debt collectors will guilt you into paying your loved ones debt. Once the debt holder dies, they're fucked.
You are under no obligation to pay for a deceased person's debt.
They will try to get you to pay any amount. Even if as little as $5, the moment you pay that small amount of the deceased person's debt (Or any), 100% of the debt is then placed under your name. And it is then your problem to deal with.
They're just trying to trick you into paying for something they can no longer collect from the person themselves.