LIMITED POWER OF ATTORNEY FOR SECTION 16(a) FILINGS Know all by these presents, that the undersigned hereby constitutes and appoints each of Thomas Burns and Bob Maddox, signing individually, as the undersigned's true and lawful attorney-in-fact to: (1) Execute for and on behalf of the undersigned, in the undersigned's capacity as an officer, director and/or stockholder of XOMA Corporation (the "Company"), Forms 3, 4, and 5 and amendments thereto in accordance with Section 16(a) of the Securities Exchange Act of 1934, as amended (the "Exchange Act") and the rules thereunder; (2) Do and perform any and all acts for and on behalf of the undersigned which may be necessary or desirable to complete and execute any such Form 3, 4, or 5 or amendment thereto and timely file such form with the United States Securities and Exchange Commission (the "SEC") and any stock exchange or similar authority; and (3) Take any other action of any type whatsoever which, in the opinion of any such attorney-in-fact, may be necessary or desirable in connection with the foregoing authority, it being understood that the documents executed by and such attorney-in-fact on behalf of the undersigned pursuant to this Limited Power of Attorney shall be in such form and shall contain such terms and conditions as such attorney-in-fact may approve in such attorney-in-fact's discretion. The undersigned hereby grants to each such attorney-in-fact full power and authority to do and perform any and every act and thing whatsoever required, necessary, or proper to be done in the exercise of any of the rights and powers herein granted, as fully to all intents and purposes as the undersigned might or could do if personally present, with full power of substitution or revocation, hereby ratifying and confirming all that such attorney-in-fact, or such attorney-in-fact's substitute or substitutes, shall lawfully do or cause to be done by virtue of this Limited Power of Attorney and the rights and powers herein granted. The undersigned acknowledges that each of the foregoing attorney-in-facts, in serving in such capacity at the request of the undersigned, is not assuming, nor is any Company assuming, any of the undersigned's responsibilities to comply with Section 16 of the Exchange Act. This Limited Power of Attorney shall remain in full force and effect until the earlier to occur of (a) undersigned is no longer required to file Forms 3, 4, and 5 with respect to any securities issued by the Company, (b) revocation by the undersigned in a signed writing delivered to the foregoing attorney-in-fact and (c) as to any attorney-in-fact individually, until such attorney-in-fact is no longer employed by the Company. This Limited Power of Attorney may be filed with the SEC as a confirming statement of the authority granted herein. IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to be executed as of December 31, 2018. /s/ Barbara Kosacz Barbara Kosacz