If you move in with your boyfriend while he's still working, your Disability Allowance payment will have to be reviewed. Because it's a means-tested payment, your entitlement will be re-assessed to take his earnings into account.
If your boyfriend becomes unemployed, he can sign for Jobseeker's Benefit (based on his PRSI contributions). If he gets part-time work, he may be able to claim some Jobseeker payment, depending on the hours and earnings.
Either of these situations can also affect your payment.