The state could reduce homelessness and save millions in shelter and other costs by finding ways to prevent evictions from public and subsidized housing, according to a report by a nonprofit housing group.

HomeStart Inc., in coordination with the Boston Housing Authority, used its report to track its efforts to intervene in evictions from public housing and to provide financial counseling to poor families. The report said Home Start has prevented more than 500 evictions from the authority’s properties since 2010, not only saving families from homelessness but saving taxpayers thousands of dollars.

In the first year alone, the program saved the Boston Housing Authority $365,000 in eviction-related costs, according to the report.

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