Is it permissible for me to use things left behind by girls who used to live with me, with the possibility that they might want them but have not returned or asked about them?

If the abandonment of these items indicates that their owners have no need for them, then there is no harm in taking them and benefiting from them. The jurists have indicated the permissibility of taking what falls from a person that they do not bother to retrieve, such as a coin or a date, and what remains in farms after their owners have left, and what falls from grains during harvest that its owner does not bother to collect, and food and rags that people discard due to their disinterest in them. Whoever comes across these permissible things first has a greater right to them and does not need anyone's permission.