Yes, you can still get infected even if fully vaccinated, known as a break through. But chances are lower , more so if the vaccine has not waned and if close to 6 months you get a booster than again lower chance.
What is equally important is that you have to continue to take the necessary precautions regardless of whether you are vaccinated i e masked up outside, sanitise and do not touch face with hands, social distancing, try to limit contact with people outside your household, try to limit eating outside, if you have any covid symptoms or had contact with someone with covid isolate immediately, art than contact moh hotline for further assistance.
Vgd advice for your parents in addition make sure they go for their boosters after 6 months or earlier depending on moh sms...also make sure they get their flu jabs as well...double protection is always vgd