Potential tenant with breaking lease 2011

[Flora Granter]

A potential tenant contacted me and was upfront that they have some credit issues including a broken lease in 2011. It happened when they have medical conditions and could not work enough hours. According to them, they have a good job and saved enough for double deposit. Would you rent to tenants like them? I asked for bank statements, pay stubs, employment verification, besides credit checks. Shall I ask for 2-month of these statements? Is there anything else I should ask for? Appreciate advice from seasoned landlords.