Can vaccinated people spread covid?

BoyMommy19 • Mommy to one beautiful baby boy born November 2019 💙

My parents are fully vaccinated but they were exposed by my sister on Thursday then she got severely sick on Friday with a 103 fever and cough. She never gets coughs. I'm pretty sure it's Covid but she won't get tested. My dad came to my house surprising me with goodies for Mother's day. I appreciate the gesture but afraid that he exposed me to covid especially I haven't got the vaccine.