Before now, this kind of issue had also been experienced by my friend. His wallet got compromised, and every valuable asset in it was moved to an unknown wallet, but there was a token in that hacked wallet that was not yet listed on any exchange (bought from an ICO). I believe it's because the token was not yet listed; that's why the hacker did not move out the token.
My friend wanted to move the token to a new wallet he has created because he knows that when the token gets listed on the exchange, it will be profitable. So, what he actually did was give the wallet phrase to about three friends and ask them to import the wallet on their device. After which, all of them had an agreement that one person among the four of them would send BNB to the wallet, which would serve as a gas fee, while the other three people would initiate a withdrawal after the BNB deposit was successful.
It was like a rescue mission, lol, but
It actually worked like that: the token was successfully withdrawn, and the rest of the left-over BNB also got automatically withdrawn to the hacker's wallet.
@OP, If the staking period of that friend's coin is due, it will be transferred back to the hacked wallet you are talking about, and if the coin is already listed on an exchange and it's a valuable coin, there is a high chance that it will be withdrawn to the hacker's wallet even before you think of sending it out. But if it is not done by the hacker before you try, I will advise you to try the technique my friends used. If it's an Ethereum-based coin, use an ETH deposit for the fee, but if it's a BNB-based coin, you can deposit BNB for the fee.
This works because the hacker don't use the automatically sending trick on the wallet already, if not, once the BNB entered the wallet it will automatically be moved into the hackers private wallet, there won't be enough time to move your tokens.
If the recovery seed is lost to a random person who have not much skills with crypto wallet you can also move the token out, I guess that's why your pals are able to move the token, OP should try moving the token out by sending $1 worth of BNB to the wallet, just to see what will happen, if the BNB also vanish in seconds then the whole wallet is compromised with the staked tokens.