I'm not overly familiar with SNAP/EBT policies, my girlfriend and daughter were on my mother in law's case(we live on the same property) but after a disagreement my wife called and removed herself from the case and created her own. The representative she spoke with told her it would not affect my mother-in-laws benefits and that next month my wife would receive her own separate benefits. Since this my mother in law has been in a rage claiming they've opened an investigation into her case over it and is worried about getting in trouble and insists that I make my wife and daughter leave for putting her freedom in jeopardy. After some digging I've come to the understanding that this is a highly unlikely scenario because her case worker to was informed after my wife left the SNAP group. I feel like she is lying out of spite and I can't seem to locate any in-depth written policies about this.
There could absolutely be an investigation of some sort, but transferring benefits is unlikely to cause a serious investigation on its own
No one is ever guaranteed that their case won't be subject to an investigation or audit, but if there is no underlying issue then there isn't much risk of consequences arising from the investigation. It's also not clear, from the second-hand report of your mother-in-law's interpretation of what is happening, what the "investigation" actually is.
In my experience helping people determine their eligibility and apply for public benefits, the "investigation" could be anything from a full audit of your mother-in-law's application, finances, and benefit disbursements, or it could have been a single phone call or letter requesting clarification on something. I saw that sort of thing happen a lot with inconsistent application details, like one person listing another member of their household as a spouse when previous information indicates that they are not married, or one application's list of financial assets conflicts with other information the benefits office has. Those would usually be very minor issues to sort out, but they generally do need to be sorted out to continue receiving benefits.
If your mother-in-law misrepresented her household in some way on her application for benefits, or did not provide updated information when her circumstances changed, and so there is a problem for an investigation to find then an investigation might be an issue for her. It's not likely, in my experience, for someone's "freedom" to be at risk as a result of an investigation like this, though it's hard to say what, specifically, your mother-in-law meant by "freedom".
However, if there was relatively large-scale and/or long-term fraud, the risks might be much greater. The most substantial risk (again, in my experience) is that she received more money than she was supposed to-- penalties could range from paying the excess back to prison, depending on the severity of any overpayments.
There are a lot of rules, which vary by state, which govern what is considered to be one household for determining benefit eligibility and amount. I imagine you've already checked out this page for some details. Without a full roster of people living in the house, their relationships with each other (and particularly your mother-in-law), their ages, incomes, assets, and so on, no one is going to be able to give you precise information on this situation. Contacting the DCBS office in your county of residence is the best way to get specifics on public benefit policies in Kentucky for a specific household.
I'm not sure I 100% understand what you mean by
After some digging I've come to the understanding that this is a highly unlikely scenario because her case worker to was informed after my wife left the SNAP group
but I can't think of any way to read it that suggests the conclusion you've reached. It doesn't matter when a given case worker found out about something, or even necessarily what happened to prompt a review of the case. If there is something that would trigger an investigation, and that thing comes to the attention of the agency that oversees the benefits, there will likely be an investigation.