Do you bear any responsibility for your car tire falling off and causing an accident to another car, given that you did not stop to check on the matter?

You should not have left your Muslim brother in that state. You must now travel to the accident site and follow up with the security authorities to ascertain the outcome of the accident. You must also adhere to everything that the Sharia (definition) court obligates you with, in terms of financial or physical compensation, unless they pardon you. If it is impossible to reach them, then you must seek forgiveness for them, supplicate for them, and increase in performing good deeds.