My wife and I are EU citizens. I am employed by a Dutch company. This company may hire my wife indirectly as a freelancer through a US based company to work remotely from home. Essentially they would pay the USA company, who would then pay her. Would she be liable for any tax in the USA?
Since the answer to this depends on issues you haven't mentioned, like your wife's country of residence, whether she has connections to the US (green card or recent physical presence there) and stuff like how the US company is accounting for the payments, it isn't possible to answer this authoritatively. However, even knowing that, the answer is going to be complicated enough that you might not get a good response here, so maybe a more general answer will help get you started?
Generally speaking, a non-resident foreigner's income from a US source will be subject to withholding tax unless there is some other arrangement which avoids that. The US payor will be responsible to remit the withholding tax to the US government, so you'll know the income may be taxable in the US when the US company takes taxes from it. Note that a tax treaty between the US and the country your wife lives in, should one exist, may reduce or conceivably eliminate the US tax payable and will almost certainly allow her to avoid being double-taxed when she declares the income in her home country, but if the company paying her takes the full withholding tax anyway the only way to get the overpayment back will be to file a non-resident tax return in the US asking for a refund on the overpayment. All of this sucks.
In any case, the place to start is probably to find out if the US company is going to be deducting withholding tax, or any other amount of US income tax, from her payments. If the answer is "no" then your wife will have no problem with the US and will only need to report the income where she lives. If the answer is "yes" then she'll be paying US taxes but may be able to get some of that back, or write off the US payments against taxes owing in her home country, if a tax treaty between her country of residence and the US exists. Unfortunately, my experience with this situation suggests that, unless she is much smarter than I am, she'll probably need to hire an expert to figure out what taxes she should be paying, and where, under the treaty.
P.S. I should have noted that if your wife's income is going to be taxed the US company will (or should) ask her to fill out an IRS W-8BEN form, which is how the US will know it is your wife who is being paid and is also where the claim to the benefits of a tax treaty can be asserted.