I've been looking into this over the last week, and here's what I've come up with.
There are several kinds of products, but you've got to be real careful, because each provider does it slightly differently. There are variations on all of the below.
Renter's Insurance covers the renter's PERSONAL property as well as liability if the renter is found liable for damage to someone or something (but only related to the five major perils in terms of your property).
Some renter's insurances cover damage to the unit but it is extremely limited. It has to be accidental, and derive from one of the major perils: fire, water, smoke, etc. Things like vandalism, negligence... none of that is included. Some providers go a bit further and cover pets, cigarette burns, bed bugs etc But the stuff we really want to be covered for as landlords, vandalism, destruction etc no one will cover.
A surety bond replaces (or augments) the security deposit. IT IS NOT INSURANCE. The renter pays a non-refundable fee of around 10% of the security deposit. This fee goes into a aggregate bucket made up of all the fees your units "produce" (this is why you need usually 100+ [for some providers 1,000+] units to make this work). The providers take a cut from those premiums as well. You then use funds from this bucket to repair damages left by a tenant. If damages go beyond the amount guaranteed by the bond (in other words what would have been the security deposit), the provider will/can start collections. However, the collections agency will take a 60% cut from what they collect (and they usually don't collect more than 10-30%). In other words, the provider carries zero risk, it's all on you. If you have 1,000+ units this might make sense, but you may as well administrate it yourself.
Anything that is called a security deposit insurance is - inmho - a misnomer. It is pretty much always a surety bond. There is a new company out of NY that seems to be doing it as an insurance, but they are a startup and they only serve NY.
Some people claim that you can make a claim against your property insurance and tell them that the tenant has renter's insurance; and that then your insurance will go after the renter's insurance. But I'm not sure if that is not an urban myth.
Conclusion: willful, negligent damages by a tenant (punched holes in walls, broken windows, graffiti etc) is is not covered.