As Zaguru12 said, it will be dropped by the nodes' mempools. It generally takes 2 weeks to be dropped if the fees don't fall below your fee rate.
There are many mempools, not only one mempool. A waiting transaction can be dropped from one mempool but it can be chosen or not drop by other mempools.
The question is seriously because it asks for chance to get a confirmation after 1 or 2 years and honestly I am not sure all mempools will not drop that transaction if it stuck like 1 or 2 years. Mempools have their max mempool size, mempool expiration time and they can update their min transaction fee too.
Chance to see an unconfirmed transaction is not dropped from mempools after 1 or 2 years is like impossible.
Firstly apogio specified that each node has its one mempool I just bolder that part.
Yes it is rare to see transaction still left in mempool for almost 1-2 years but it is much possible either by the user himself rebroadcasting it regularly and the fee as stated above or the wallet used as an inbuilt rebroadcast which it does regularly. This will make the nodes that have dropped the transaction to pick it again and could remain like that except if the fee paid was at one time ok to get it confirmed