Help Prevent Homelessness for a Hardworking Individual

I would have never dreamed we would be facing homelessness. Due to unfortunate circumstances in the last few weeks, I am faced with financial difficulties and I have had many sleepless nights trying to figure out what to do. I have reached out to government programs and was pretty positive they could assist us; however, they take your gross income and I am barely over, while my take-home is less. Being denied has been crushing as I am not one to take handouts in this manner and I have no idea what to do. I am in the midst of trying to find a roommate to be able to keep in our current living space, as there is a huge lack of housing availability and safety concerns in areas. We are behind on July rent and due to the time it takes to vet a roommate, August rent assistance would be appreciated. I believe I can make it going forward after August. I am terrified by this situation and humbled by any support anyone can help us with. I am a very hard worker and a good person. Thank you all