I don't know the exact time but usually a week nodes should reject it but better to ask the sender what wallet he used to send the BTC
Because some wallets like Blockchain wallet it always rebroadcast unconfirmed transactions same goes for exchanges.
On Bitcoin Core, it is 14 days by default. But node runners can set it to what they want.
That only works if you fully trust the sender to do so.
If it is me and I do not trust the sender, that means I will not give the sender what he wants in exchange for the money. It is cash and carry or we should use escrow. I will tell the sender to pump the fee.
Also, why telling the sender to make another transaction and not just rebroadcast the same?
I think that is what he meant. To resend the coin again in a new transaction. But nice making it clear because a coin that is thought to have been dropped has not been dropped from some other nodes and if the fee rate becomes lower, the transaction that has been thought to have been dropped can later be confirmed.