Yes, both sentences are correct.

In your first example, please note your sentence means "she ate herself". If you wanted to say that you ate her, you can use the following instead:

• Il y aurait une femme en pain d’épices. Elle s’est fait manger.

Other examples with this structure:

• " se faire laver " : having someone wash you
• " se faire prier " : having someone beg you (to do something)
• " se faire voler " : having someone steal you

And so on, any verb will match.