Are people who are born with brca gene at a higher risk for recurrence of cancer too?

Not Exactly: Breast cancer may recur either in the breast ("local recurrence") or elsewhere in the body (distant metastasis). The risk of metastasis varies from very low to high, and is correlated with the stage of the cancer. Local recurrence following lumpectomy and radiation therapy is less than 5%. However, brca(+) people do have a (much) higher risk of developing a second primary breast cancer.

Yes!: If you have a mutation in the brca gene, you are at higher risk of getting a first cancer, and of having recurrence of a prior treated cancer. The brca gene helps cells repair themselves when they get damanged. Cells in people with a mutated brca gene can't repair themselves, so they are more likely to become cancerous. I keep a very close eye on my cancer patients with brca mutations!