A person's debts don't disappear when they die — they pass to the heirs. In Slovakia, though, there's an important protection many people don't know about: an heir's liability for the deceased's debts is automatically limited to the value of what they actually inherited.
If you accepted the inheritance, you're only liable for the deceased's debts up to the value of the property acquired — no more, and not out of your own pocket. If the deceased left no property at all, you inherited nothing and don't have to pay anything from your own funds, even if all they left were debts. You don't need to actively invoke this protection or request it — it applies automatically by law (§470 of the Civil Code).
Since liability is capped at the value of what's inherited anyway, renouncing mostly makes sense when you want to avoid any communication with creditors at all, or when the estate is real but of low value and the process would bring more hassle than benefit.
You can only renounce the inheritance as a whole — property and debts together, you can't pick just the favorable parts. The deadline for renouncing is one month from the day the notary or court notified you of the right to renounce the inheritance (§464 of the Civil Code) — not from the deceased's date of death. If you live abroad, the court may set a longer deadline.
This deadline is substantive — the declaration must reach the notary by the last day of the deadline at the latest; it's not enough to simply mail it that day. It runs separately for each heir. If you don't renounce within the deadline, an irrefutable presumption applies that you accepted the inheritance.
Heirs can also protect themselves another way — at their request, the court summons creditors to file their claims within a set deadline (§199 of the Civil Non-Contentious Proceedings Act). Creditors who don't respond despite the summons risk losing the chance to be paid if the value of the estate has meanwhile been exhausted.
This is a general description of the statutory framework, not legal advice for your specific case. If you have a real concern about the deceased's debts, we recommend discussing the situation directly with the notary handling the proceedings.