gloria the homeless cannot claim universal credit even for emergency accommodation. No one who is homeless, including families can. You must have a permenant contract for housing (minimum six months) to claim anything. That applies to everyone. They get nothing. Those living will families can claim individual components because their housing is free.
Exemptions are used so people think what you are. Did you know if someone in this group gets thrown out they must pay for mediation to be considered for housing? If they've had abusive homes and their family haven't been arrested and prosecuted they must go through mediation? DV? Same thing. Leaving care rule literally applies when you walk out the door from the care home, not retrospectively.
It's run by local authorities and mine is determined no one gets a penny if they can help it - example the number of bedrooms in a property in my county includes any room which meets a set criteria of size and a window, so literally you get a bedroom if on your own. In a bedsit you get one bedroom rate, in a flat with a lounge that's classed as two.