Then it is best to contact your management company if you have one, or read the proprietary lease if self-managed, to see who is responsible. Generally if in the walls, it is the co-op, if inside, it is the unit owners.
Also, contacting the co-op insurance company won't hurt either.
Lastly, the owner of the damaged unit should at least notify their insurance company of the damage. They usually will pay the unit owner for damages and then fight it out with the other insurance company, in this case, the co-op's insurance company, to get reimbursement.
If you are talking about damage to your personal belongings, that would only be covered if you had your own policy. you would have that just like you would have a renter's policy if you are a renter. Requiring a "walls in" policy might be coming soon, as it recently became a requirement of those getting loans to buy condos.
Is it the coop's plumbing that caused the backed toilet or did the share holder flush something down the toilet. Most coops recommend or require the share holder to have home owner's insurance for this reason. Home owner's insurance will cover it. Coop's master insurance probably not. They may fix the plumbing but they probably will not pay for the damages in the unit below.
Contact the super, building manager or managing agent to find out.