What is the ruling on taking two pieces from an abandoned fishing net and selling them, and what is incumbent upon the one who did that?

The situation does not fall outside of two cases:

The first: The strong presumption is that its owners will return. In this case, taking it is an injustice, and it is obligatory for you to repent and return the money to its owners, or to give it as charity if it is impossible to reach them.

The second: The strong presumption is that it has been lost (like a lost item - luqatah). If its value is small, there is no harm in selling it and disposing of it. However, if it has significant value (which is apparent), then you erred by disposing of it before announcing it for a year. It has now come under your guarantee, and its owner has the choice between reclaiming it or its value, or approving the sale and taking the price.