According to the search results, the percentage of homeless individuals who have a serious mental illness is estimated to be around one-third. However, it is important to note that this percentage may vary depending on the age group, how homelessness is defined, and other factors. For example, a 2019 survey found that only 26% of unsheltered homeless individuals reported mental health issues. Nonetheless, it is clear that mental illness is a significant issue among the homeless population, and many homeless individuals with mental illness are not receiving the treatment they need.