What happens if a Beneficiary of a Trust doesn’t pay income taxes from a K-1 Inherited IRA Distribution?

This is a hypothetical question but I am just curious. Let’s say that the beneficiary purposely doesn’t pay income taxes to the IRS from a K-1 Inherited IRA distribution. Will the IRS go after the Trust for the beneficiary’s taxes? If so, it’s just one more reason not to close out a Trust prematurely and to have monies available for such a situation or else the Trustee will be responsible.