To the best of my ability to remember, I never heard the word busking before reading it in A Long Way Down. Web search says the term busking originated in England. Makes sense; author of the novel, Nick Hornby is English. Busking is what I call street musicians or perhaps more correctly what street musicians do ~ play a guitar, case open in front of them on sidewalk, expecting or hoping passerby's toss some coins there way ~ or more preferably dollar bills.
Character in the book, JJ started busking because it felt better than delivering pizza. He had competition from Jerry Lee Pavement who would set up next to him, playing the same tune JJ was playing. Earlier, JJ, his band-mate/brother, and ex-girlfriend took an argument out on the streets. A homeless guy joined the sparring. JJ imagined the band getting back together dedicating a song to "Homeless Guy", and "Hey--he could maybe even be our road manager."
The homeless guy in the book probably was not suicidal. Does not specifically say that Jerry Lee Pavement was homeless. There have been incidents were people jumped to their death from not-so-tall buildings in Long Beach. It seems to me, the preferred manner of a homeless person taking their own life in Los Angeles county is to step in front of a moving train.
I always wondered if the dead person found in a beach seaweed hill was a guy whose name I have forgotten, perhaps it was John. Last time I spoke to him he wanted to get a hemlock rope and end it all. The body found in the pile of trash raked up from the beach was his age. I pretty much read the Press-Telegram daily while on the streets and did not see a follow-up story identifying the dead man.
Feeling worthless with no hope does lead to suicidal thoughts. I doubt, though, that homeless people are more prone to them, than any in the general population.