Yes, especially if you've spoken with the nursing home's staff and they indicate a level of neglect. If you win your case, insurance should cover the claim, as long as the nursing home is insured. If the nursing home is uninsured, they will either have to pay the damages itself or the award would be uncollectible if the facility did not have the finances to pay.
When you bring a claim against a nursing home, the insurer will be notified immediately. If there is no insurer, you will be dealing directly with the nursing home, if they can afford to respond to your claim.
In either situation, you should have the advice of an experienced attorney instead of trying to negotiate a claim on your own.
An attorney can determine what the insurance policy limits are and what the potential value of a claim is so you do not go in expecting more than is possible for a recovery or do not undervalue the case and agree to a low settlement. You also need to make sure you are fully aware of all your rights and the rights of your loved one.