We often hear about our money that you can't take it with you, but when it comes to debts, you can leave them behind.
The debts of your girlfriend
and her funeral expenses are exclusively her debts. Those debts belong to her estate and not to you regardless of how long you may have lived with her. If, however, you agreed with the funeral provider to be personally responsible for her funeral costs, you may have a problem there. But if you only acted on behalf of her estate, you do not have a personal liability for her funeral costs.
A person's debts and final funeral expenses are required by law to be paid from their assets before anything is distributed to their heirs. In the case of your girlfriend, it appears that her only asset is her share of the real estate. It is from that asset that her debts and final expenses should be paid. The life insurance policy that you carried on her life naming you as the beneficiary of the policy is not a part of her probate estate and is not required to be used by you to pay for any of her debts and expenses.