Octomom -- Offered Free Security Following Death Threats

The death threats Octomom received after news broke she had gone on welfare were so bad ... that a few security companies have reached out to her offer up free protection services for her and her family ... TMZ has learned.

As TMZ first reported, Octo had her car window smashed in with a handwritten note that said, "Leave California or you will die!" The threats started after TMZ reported Octo began receiving $2,000 a month from the State of California, which could only be used for food.

Sources close to Octo tell TMZ that numerous security companies have stepped up to offer her free protection. We're told they have offered 24/7 security guards, multiple people for the kids -- all for free until she moved to a new home, the location of which will be secret for as long as possible.