The government did not “heal” the Great Depression, it caused it. It was caused by the government artificially lowering interest rates. During the Great Depression the government increased the minimum wage a lot. Prices were falling at this time so it was basically like the workers were getting a raise and the businesses couldn’t afford to hire as many people leading to more people being unemployed.
The Housing Bust of 2008 was certainly caused by the government. Fannie Mae and Freddie Mac would buy mortgages from banks. Bankers began to realize they would buy almost any mortgage, so they allowed many people without jobs and money to buy houses and use mortgage loans. Eventually a lot of the risky people would not pay their mortgage payments, so the federal government would print more money to give to Freddie and Fannie. These bailouts and the increasing demand for houses caused higher prices to keep rising and it led people to believe buying houses was great because their value kept rising. Eventually Freddie and Fannie defaulted and the thing collapsed hurting many people who bought homes because their values dropped dramatically.