While most notes waive notices of dishonor and presentment or default allowing demand for cure, notice of default can be public notice.

In this case, the lender likely figured they would cure the lien if they had to in the event of default by the owner, to protect their ability to foreclose and sell the asset to recoup their loan amount and fees. 

Say they are in violation of the lease agreement and include legal "Three-Day Notice to Cure" language.

I dunno how long in your state but in Colorado a fairly land lord friendly I figure a little over a month if I give the cure or quit notice on the 6th of the month.

The dehumidifyer will cure any smell in the basement if it is on, which it has not been due to no power.Threatening to take me to court if not return her deposit.Now may take me months to rent out again. 

If the investor is paying cash and can cure the deficiency and bring the loan out of foreclosure status obviously w/ room to do the deal like any other then would there be any problems from the lien holder?

You absolutely should contact a local Real Estate attorney to discuss what options you have to cure any deficiency on the title, and what remedies you may have against the Title Company for failing to properly close on the property.

If there's mold, get a mold remediation company to write up a report and the cost to cure it.

If you can cure it quick enough, your long-term tenants may use this as an excuse to break the lease, or they will move when their lease ends.

If I serve a 3 day notice to quit or cure how do I prevent Cozy from accepting partial payments?