Is it permissible for me to contract with clients of my current company, whose business has deteriorated due to mismanagement, after these clients request me to do so?

If you are still bound by a contract with a company, you are not permitted to deal independently with its clients, because this is considered a forbidden sale over the sale of your Muslim brother. Ibn Taymiyyah emphasized that renting over the rental of one's brother is even more harmful. However, if your contract with the company has ended, or they consent to it, then there is no harm in you dealing with any clients.