Something doesn't add up here, and you might not have enough information to figure out what's really going on. You said the business was an LLC, and your ex-husband had no partners. But an LLC with only one owner, which is called a single-member LLC, doesn't issue a K-1. The business income and expenses are reported on Schedule C in the owner's tax return. Is there a Schedule C in your joint tax returns (before the change to a W-2)?
There are three different kinds of K-1. Do you know what kind you had?
A Form 1065 Schedule K-1 is for a partnership. That would mean there was at least one other partner. A multi-member LLC is treated as a partnership for tax purposes. It's quite possible, and legal, that he would not get a W-2 from a partnership.
A Form 1120-S Schedule K-1 is for an S corporation. The LLC could have chosen to be treated as an S corp for tax purposes. But as tagteam said, an S corp owner is supposed to be paid a reasonable salary. If he was getting a salary from the S corp he would have gotten a W-2 in addition to the K-1. So either it wasn't an S corp, or he wasn't following the rules.
A Form 1041 Schedule K-1 is for a trust. I don't know much about trusts. If the LLC was held in a trust, it was probably some sort of scheme to reduce or avoid taxes. It could also be a way to hide income or assets from you and the IRS.
Were the K-1s and the W-2s from the same company? It's possible that an LLC that was being treated as an S corp changed to being treated as a C corporation, and your ex became an employee of the C corp. Then he would have gotten a W-2 and no K-1, because a C corp does not issue a K-1. The C corp files its own tax return, but does not show up on the owner's personal tax return. So that could be an attempt to hide income or assets from you and the divorce court. He could have let additional profits, above his W-2 salary, accumulate in the C corp, then taken it out later after the divorce was final.
The IRS is aggressive about going after S corp owners who do not draw a salary. If that's what he was doing, the IRS might yet audit him - and you - for that issue. Even though you were not an owner of the S corp, you are equally responsible for any underreporting of income on your joint tax returns. There is a such a thing as an "innocent spouse," who did not know, and had no reason to know, that the other spouse was cheating or omitting income. But if you filed a tax return with a K-1 from an S corp, or an LLC treated as an S corp, and no W-2, you had reason to know that something was wrong. You would have a hard time convincing the IRS that you were an innocent spouse.
