The interior and weak foliage usually turns brown when it dies. If it dies during a frost, they can turn purple and then a mushy black.
That's a normal process. But it can look unsightly.
If it expands into the healthy green, it's a reason to investigate. Keep an eye on it, and report to us if that happens. Not that there's much you can do during the cold season, but it might indicate a you'd need to change a plan the next growing season.