What is the ruling on receiving a short supply of medicines, knowing that the previous employee is responsible? And is it permissible to have health insurance with the intention of not using it?

There is no blame upon you for receiving the trust (custody), and you become responsible for whatever is missing from it after your receipt. As for insurance, its ruling depends on its type. Commercial insurance is forbidden and it is not permissible to participate in it voluntarily. If you are forced into it, then the sin is upon the one who forced you, and it is permissible for you to benefit to the extent of your contribution. As for cooperative solidarity insurance, there is no blame in participating in it and benefiting from what it provides, and there is no blame upon whoever chooses not to benefit from their right in it.