I have never seen a 3+ month notice to quit in the country I live, curious which country this happens in? Sounds extremely ridiculous if true
You can ask your employer to let you go sooner if you want to leave, and they may ask you to leave sooner if they want you to leave (and pay you as an incentive). But it has to be by mutual agreement.
Usually they’d let you go sooner rather than later because they know you’ve already left mentally and they don’t want to pay for that. But they might also not, not necessarily out of spite but because they have a deadline and they think they still need your warm body.
Not that I complain, six months of rest and vest life wasn’t bad :-)