Is it permissible for the husband to take gold or money he finds inside used clothes that he sorts at his job, given his difficult financial situation?

The basic principle is that gold and money found in used clothes are considered lost property (luqatah). Your husband is responsible for publicly announcing them and returning them to their owners if they can be identified.

However, if the owners cannot be identified (which is usually the case), some scholars hold the view that the finder may take ownership of it without public announcement, as announcing such trivial amounts would be futile.

This money can also be spent on the welfare of Muslims. If your husband is in need, he may take from it according to his need. Any surplus should be spent on general Muslim welfare.