A more practical question might be "how can I get rid of the rats?"
Report the condition to the New York City Department of Health and Mental Hygiene either by calling 311 or using the link below.
After they investigate, they will give you more information.
In New York, the Statute of Limitations for breach of contract is six years except for contracts for the sale of goods in which it is four years. In either case, they are within the limits.
Be advised that there are several law firms in the city that do nothing other than handle hospital collection lawsuits and that hospitals are not shy about suing people.
If the bill is legitimate, now is the time to see if there is any way to negotiate a reduction, or failing that, a payment plan....
Oral (not "verbal" by the way since almost all contracts contain words) contracts are sometimes enforceable if they meet the requirements of a contract and the facts of the making of the contract can also be proven.
In your case, if the company is located in New York City you can get help from the Department of Consumer Affairs. If elsewhere in the State, from the NYS Attorney General's Office.
Where are they?
In order to answer this question, it is necessary to know the exact location of the property. There could be a state law, a local ordinance or even a homeowners' association covenant applicable to the property.
See a local lawyer.
There are two questions that need answers and for them you will need an attorney in your state:
1. Is there a lease provision applicable to this situation?
2. Is there a state or local statute (commonly called a "roommate law") that pertains to your situation?
Even though I specialize in retail leasing, I cannot answer this question without seeing the lease.
Lawyers cannot interpret documents we cannot read.
Take the lease to a California lawyer with the needed expertise.
It seems like your sister was a tenant of her in-laws, hardly grounds for an adverse possession claim.
Besides that, here are a few questions:
1. To whom were the real estate tax bills sent by the Department of Finance?
2. Does there exist any writing between the owners and your sister with respect to her "residency" on the property?
3. Did they ever ask her to leave and if so, did she refuse?
4. Is there (or was there in the past) a mortgage on the...
First question: WHY are the tiles getting damaged?
Next question: Whose responsibility is it, the landlord or the tenant above?
You can answer the first one and then a lawyer can read your lease and help you with the second one.
Another thing you can do is see if any insurance you have covers this.