That depends on what the Court Orders. Sometimes, the sanctions amount to assessing only
attorney fees ?? The Judge alone decides. You should not be concerned, because you
are not the party responsible.
Ohio may have "special" laws for foreclosures. Better check the law for OHIO !!
I apologize but not clear if you are asking if the mediator has ability to ask judge to dismiss, or that the mediator has already asked the judge to dismiss. Generally in mediation, including court ordered, the mediator's role is to bring parties together in settlement and if a party refuses to participate, the mediator is limited to reporting to the judge that there is an impasse. In the jurisdictions where I practice, a mediator does not recommend dismissing a case, or other action to a judge, but simply reports if agreement was reach and case settled or not settled (impasse) then case proceeds in court.
A party should not be requesting information in a mediation the mediator's role is as a facilitator not a decision maker. Providing evidence or documents beyond what is needed for mediator to understand case and work with parties, is counter productive.
Another issue is that new evidence, documents or statements by parties in mediation are confidential and if case does not settle can not be used in the trial. This confidentiality is a key component to helping bring parties together to settle. It allows them to be forthright in discussions without fear of the other side using what they say in the case.
I am NOT admitted in Ohio but what I explain above is generally applicable in most jurisdictions based on my experience.
If the judge does dismiss the case, what happens to you will depend on the judge's order, as noted in the previous comment.