Navigating Finance Issue More Than Years' Income?

I and my family have been saving monthly for housing expenses (both annual upkeep and preparing for major repairs such as replacing water-heaters, foundation-repair, and other after-a-long-time-starts-to-break-down). However, our foundation is beginning to become concerning, and we are nowhere near savings amount to pay even half.

Would a foundation repair [bid about $32,000] be considered a financial emergency? I have emergency savings…but I'm not sure if I should use it towards a down-payment [to lower the cost of monthly payments for the fix].