Unless they land an extremely lucrative gig that pays cash or on a daily basis they won’t have enough money for a deposit for at least a month if not a few months. Employers typically only pay every two weeks so they would be without any funds for at least that much time. Within that time they will still need three square meals and that will be difficult to do if their work schedule conflicts with when the shelter provides meals and it will be especially daunting if they are assigned night shifts by their employer that conflict with the curfews set by the shelter. I actually answered this question in detail five years ago.
The Link Between Homelessness and Labor Force Participation
Employers also prefer not to hire people who use shelter addresses on their application which is why most homeless who are employed are either employed through temp agencies or are embroiled in the gig economy; both avenues make long term employment difficult to sustain. A cross sectional analysis counted by Meyer et al., based on data aggregated from the Census Bureau’s 2010 Service Based Enumeration Survey, American Community Survey, HUD’s Homeless Management Information System, and their 2018 point-in-time count, found that 40.4% of unsheltered homeless persons and 52.8% of sheltered homeless persons had 1040 or W2 tax forms indicating formal employment. There is also a large proportion of homeless persons who have informal employment through gig work or day labor paid under the table that does not get reported to the IRS.