After Betelgeuse die he became some sort of quasi spirit himself allowing him to possess those who are spirit compatible or lacking in sanity, in this case the fingers , Subaru and skip by the anime, Julius (The guy got his own issue).
Julius however cannot be possessed due to having six guardian spirits. This did not allow him to choose Julius as a host after the last of the fingers were eliminated but instead tried for the next best thing which is Subaru. if he did tried to possessed Julius. Betelgeuse must fight against the other six spirits and that can cause severe pain to the mind of the host which may cause him to be ejected and die for real.
Subaru to was having the same problem like Betelgeuse but we saw it much clearly, severe headache when the spirit try to cleanse him of Ram illusion
Even when Subaru has IA ,Julius lesser fire spirit to help him Subaru is not the true pact wielder of the spirit making him vulnerable to possession.
But still wanting Julius as a body due to his more powerful body Subaru was taken hostage to try to get Julius to get rid of his pact , not wanting Julius his friend (and himself) getting possessed and wreaking havoc he ask to be killed by Felix . Felix in turn ruin Subaru Gate causing his blood to boil (see episode 5 death) and Julius tearfully end his life for that loop.