That office never closes. The Church's work of mercy can never be interrupted.
However, if you think that the Church has fallen completely and can no longer absolve, why are even you bothering to ask? ( Personally, I doubt that is what you are suggesting. I'm just being rhetorical, here. )
Is sacramental grace dependent on the worthiness of the minister? If so, when did that become a doctrine of the Faith?
Does even the SSPX formally proclaim "invalidity" regarding sacraments not provided by its own priests/bishops?
Look, I know this is delicate and touchy but it is just plain nuts to think, and in a very un-Catholic fashion, that Christ has abandoned sinners who seek his mercy through official channels, even if the ministers did turn out to be - objectively - material heretics. And for tens and tens of thousands of priests and even some bishops, even if the doctrines to which they subscribe are based - IN PART - on the horrible mess created by the council and some looneytune papacies in the past 50 years, are we to consider ALL of them to be no more than Lutherans or animists when they DO believe in transubstantiation, penance, the Creed and all the sacred mysteries held by the Church since immemorial time? Who has even been around to teach them, unless they ever even heard of the SSPX? Which most never did, I'm quite sure. At least not before they answered their vocational calling.
Our own era is NOT the first to ever deal with heresy, unworthy ministers or lying. And yet, in both the Church and the Society - which is PART of the Church - grace flows and neither one is free of heresy, unworthy ministers or lies.