“Free Money” – Taking money from the government (food stamps, welfare, Medicaid, etc.) to stay in Kollel

Is it permitted to not disclose off-the-books income when applying for government benefits?
What if there’s a colorable argument that you fit the criteria? Is that enough?
Are there any Heterim to take funds when you don’t fit the eligibility requirements?
Is putting yourself in a position that you need to take money from the government allowed? Is it le’chatchila to take government assistance in order to stay in Kollel?
Is it a chilul Hashem if many frum people receive government assistance, when it’s not intended for those who can work?