Or the soap might firm up as normal. Whether the soap stays soft or firms up quickly depends on the recipe, temperature during saponification, water content, etc. as well as the thickness of the batter when poured into the mold. I usually pour batter at thin to medium trace, but sometimes the batter ends up thicker for various reasons (out of practice, new fragrance, the phase of the moon). All tend to behave about the same, as long as I'm using the same blend of fats.
For example, I made 2 batches of the same recipe yesterday. I poured them both when they were thicker than my preference. I can't say they're any firmer this morning than previous batches of the same recipe that I poured when the batter is thinner.
People, especially newer soapers, sometimes do get into trouble when batter is poured into the mold at emulsion to thin trace -- There is there is a little more chance the emulsion may fail so the soap separates in the mold, especially if the soap maker is a "more water" soaper and also if they keep the soap fairly warm while saponifying. There is also a slight tendency for the soap, if poured when thin, to be a bit more zappy on the bottom and not zappy on top because the soap is not quite at a fully stable emulsion when poured. This will cure out, so it's not a major issue, but something to be aware of.