'carry the stigma' is correct and usable in written English. You can use it when you want to refer to a long-lasting, negative effect that someone faces for having done something wrong, embarrassing, or socially unacceptable. For example, "Being arrested for a DUI carries the stigma of being irresponsible."
"Morris dancing won't carry the stigma of embarrassment it does in the UK.
Perpetrators have visibly scarred rape victims to ensure they carry the stigma.
And seeking pastoral counseling does not carry the stigma that seeing a mental health professional might.
But brainwashing doesn't carry the stigma it did 45 years ago.
One day soon, our greed for aerial mass transit will carry the stigma once attached to the slave trade.
"I want to make people realise that you have to make yourself heard rather than carry the stigma and hide.
"Trade" carried the stigma of commonness.
Being unemployed no longer carries the stigma it once did.
Along with the scar, he carried the stigma of epilepsy's unpredictable attacks.
These rules say that getting a whip ban carries the stigma it always should have.
And therapy no longer carries the stigma of being damaged that it used to.
I love the desktop app, it’s always running on my Mac. Ludwig is the best English buddy, it answers my 100 queries per day and stays cool.
Cristina Valenza
Retail Lead Linguist @ Apple Inc.