Not sure I should answer a post with a "how exactly" in it, to be honest, because it's rude. But:

I don't, but that negative emotion shouldn't necessarily be guilt.

First off, we don't know the obligation can't be fulfilled in this case. No reason to feel guilty if it can be. Things change.

Second, if there is genuinely nothing you can do to fulfil a moral obligation because of systemic issues, there is no value in guilt; it's literally not your fault. There might be negative emotions but it's better to consider them sadness or helplessness, and push away guilt.

Negative emotions happen. But taking on guilt for things you did not do and cannot fix for reasons outside your control is significantly emotionally damaging.