...you mean the lye solution will always bond with the oils in a batch, and there will never be free floating ones that didn't find an oil match?...
Nope, I didn't want people to think either of these things. I regret I wasn't clear enough -- let me try again --
There can most definitely be excess alkali in soap. The excess alkali can be a temporary problem that resolves itself with time. Or it can be a permanent problem that perhaps can be corrected, typically by rebatching. Sometimes the problem is bad enough the soap really needs to be discarded, however.
A few reasons why soap can contain excess alkali -- if saponification isn't quite finished (likely your problem), if the soap maker chills the soap so much the cold really slows saponification down, if the soap maker makes a measurement error and adds too much alkali, if the amount of mixing is not sufficient to intimately blend the fats and alkali to ensure full saponification, if the soap overheads and the batter separates, etc.
Soap can be temporarily too alkaline (zappy) to be skin safe if you test the soap in the first few days after it's been made. This is especially a problem if you soap at cool to cold temperatures. Newer soap makers tend to leap into rebatching soap with a temporary excess of alkali like this, but if a person can muster the patience, the problem often resolves itself with time. I suggest people wait a week or so before testing their soap -- it's very likely a soap that is slightly zappy at first will be fine after a few days.
Soap can be permanently too alkaline if you use a lot more alkali than the fat can consume during saponification. Or if the soap emulsion fails and the soap batter separates in the mold. This is when a rebatch can be useful to correct a serious problem.
Once NaOH is dissolved, it will not not magically turn solid again in the lye solution. If you KNOW your NaOH is fully dissolved and liquid when you poured it into your soap batter -- say you pour the lye solution through a strainer when you add it to the fats -- there simply won't be any solid NaOH particles in the soap. If you do see solid particles in the soap batter or the finished soap, the particles are something other than solid NaOH.
It might be possible for solid NaOH particles to be in the finished soap if something happens so the alkali can't dissolve properly before it is poured into the soap batter or the soap maker doesn't check to ensure the alkali particles are fully dissolved.
This problem can happen if the soap maker tries to chill the water or the lye solution too cold, so the NaOH can't dissolve properly. Or theh soap maker gets in a hurry and doesn't stir the NaOH particles so they remain loose and floating in the liquid so they can dissolve easily. Or the soap maker doesn't allow enough time for the particles to fully dissolve. Or they make the lye solution with an opaque liquid like milk. Or they get in a hurry and use the lye solution without checking first for solid particles in the bottom of the lye pitcher. In these instances, I can see larger particles surviving in the soap to cause problems later on.
Before the alkali fully reacts with the fats or with the carbon dioxide in the air, any liquid weeping out of the soap is very likely to be alkaline (high pH) but that liquid isn't JUST lye solution.
The weeping liquid is a mixture of all the water-based liquids that went into making the soap. We add a variety of water-based liquids to soap -- lye solution, sometimes sodium lactate, food purees, and other water-based additives. And there's also the glycerin produced from saponification which is also water soluble. Each of these water-based liquids doesn't float around the soap as an individual blob, they all get mixed together into a whole. This mixture of water-based liquids is what weeps out of soap, not just the lye solution.
Sometimes soap makers add fragrance or other hydrophobic liquids at trace. (Hydrophobic = "water hating." In other words, liquids that don't mix with water.) Sometimes the soap maker doesn't get the fragrance intimately mixed into the soap batter due to lack of time, or due to the soap batter getting too thick, or whatever. If this happens, droplets of the fragrance can weep out of the soap later. Even in this case, the liquid isn't usually just fragrance. Some water-based liquid usually also weeps out with the fragrance. The result is these weepy areas can be strongly alkaline (very zappy) at first until the alkali reacts with the CO2 in the air.