BOI's 6, 12 and 18 Month Advantage Fixed Term Deposit Accounts allow 25% to be withdrawn at any time during the term.
Raisin have a 3 month term account which allows early termination (currently offering 2.12%). They have an identical 3 month offer with the same provider which offers 2.27% and no early termination. So you are accepting a .15% penalty up front for the early termination facility, whether or not you use it.
For other Raisin Fixed Term accounts, there isn't one answer as the possibility of early termination varies depending on the bank/product you choose. So for example
Aareal Bank AG's 5 Year Fixed Term offer has the following in the T&Cs:
6. Withdrawl
For early termination of the term deposit after the expiration of the 14-
calendar day revocation period, you should send an electronic request via the
Raisin Bank Platform. Raisin Bank reserves the right to accept or reject each
request on a case-by-case basis and will contact Aareal Bank in this regard.
Raisin Bank accepts a request for early termination only for a reason that is
compelling in the opinion of Raisin Bank and only for the entire deposit. In
case of early termination by the customer, pro rata interest shall be paid for
the period between account opening and termination. The original deposit
amount including accrued interest will be refunded to the customer’s Raisin
Account within reasonable time.
Whereas
Privatbanka a.s.'s 3 Year Fixed Term offer has the following in the T&Cs:
6. Withdrawl
The deposit is not available during the term.
So if you want to know what Raisin's stance is you need to choose the Bank/Product first and read the Terms & Conditions.
I've looked at the conditions/wording that AIB and PTSB use and it also varies and is very unclear. In my opinion, your granny's funeral bill would almost certainly not be considered exceptional as you could get a loan or defer the payment - most funeral directors will happily screw interest out of you. A diagnosis of terminal cancer bringing about sudden major expenses or your imminent demise might however get a hearing. But the banks do not give examples, and make it clear that the bar is high, entirely at their discretion and may come with significant penalties, such as foregoing interest.
As
@Lightning advised, if you opt for fixed term, treat the money as gone for the duration. If in doubt, either go for a demand or a shorter term, or split it say 50/50 between fixed and variable accounts.
BTW, the penalty for early withdrawal in the case of State Savings (in the form of interest foregone) is draconian.