Is it permissible to associate with and speak to a person who is negligent in prayer on the grounds that he is always in a state of major ritual impurity (janabah)?

You must gently explain to your colleague the danger of abandoning prayer, and that it is an act of disbelief according to the preponderant opinion of the scholars. You should also ask him to perform ghusl if he is in a state of major ritual impurity (janabah) in order to pray. As for interacting with him and sharing lodging, food, and the like, there is no harm in it; in fact, it is better than shunning him these days, because shunning might not deter him. Perhaps Allah will guide him through your interaction and persistent advice. However, if shunning him will deter him, or if interacting with him will negatively affect your faith, then in that case, you must shun him.