How can a word for 'the act of Xing', semantically shift to mean 'the thing Xed'? isn't a duplicate. I ask about obligation, never mooted at How did 'consideration' semantically shift to mean 'something given in payment'?.
Perhaps it's not a duplicate, but it's not clear to me how your question could reasonably be answered.
A priori, any word can undergo a semantic shift to any meaning. As far as I know, there are no known "laws of physics" that would prevent any particular word from undergoing any particular shift. But since you're asking "how can the word 'obligation' shift to mean 'the thing one is obliged to do,'" you must have some reason to think that this shift would not happen. The only way we could possibly answer the question of "how can that happen?" is to refute your reasoning why it would not happen.
(By way of analogy, suppose someone asked, "How is it possible for the English word for Felis catus to be 'cat'?" There's no reasonable way we could answer this. But suppose they went on and said, "I thought that words for animals in English had to start with a vowel." Then we could answer this question by pointing out that English has no such rule.)
So, for your question, I'm guessing that your reasoning is that in order for a word to undergo a semantic shift from X to Y, X and Y must be similar concepts—not merely closely related, as the concepts "act of considering" and "thing considered" are, but actually similar.
But I can't think of any reasonable way your question could be answered, besides merely saying, "Actually, words can shift to meanings that aren't similar."