Short answer. No. Rule 7, Section 3 of the Rules of Court states directly that the lawyer or law firm cannot pass on the monetary penalty to the client. A sanction for an abusive pleading is imposed on the counsel who signed it, and the cost of that sanction has to stay with them.
What the law says
The lawyer or law firm cannot pass on the monetary penalty to the client.
Rule 7, Section 3 — Signature and address. Read the full provision →
Why the signature matters
Rule 7, Section 3 requires every pleading to be signed by the party or by counsel, and that signature is not a formality. It is a certification: counsel is representing to the court that the pleading was read, that it is not being filed to harass anyone, cause delay, or needlessly run up the cost of litigation, that the legal positions taken are warranted by existing law or a good-faith argument to change it, and that the factual claims have or will have evidentiary support. That certification is the lawyer's own representation to the court, made in a professional capacity, which is exactly why responsibility for breaking it falls on the lawyer rather than the client.
What happens when the certification is violated
If the court finds, after notice and hearing, that this certification was violated, it may impose an appropriate sanction on the attorney, law firm, or party responsible, or refer the violation for disciplinary action. The rule specifically contemplates a law firm being held jointly and severally liable for a violation by one of its partners, associates, or employees, absent exceptional circumstances. Available sanctions range from a non-monetary directive to an order to pay a penalty in court, and, where sought on motion and warranted for real deterrence, an order to pay the other side's reasonable attorney's fees and expenses caused by the violation.
The client is shielded from the monetary sanction
Whatever monetary penalty the court imposes under this rule, the text is direct about where the cost has to land: the lawyer or law firm cannot pass on the monetary penalty to the client. The sanction exists to deter the lawyer or firm from certifying an abusive pleading, and shifting that cost back onto the client who relied on counsel's professional judgment would defeat the point of imposing it on counsel in the first place. If a lawyer has attempted to bill you for a sanction imposed on them under this rule, that charge runs against the rule's own text, which places the obligation squarely on the lawyer or the firm.