At eleven o'clock at night on April 4, 1888, at the age of 75, Dr. José Eleuterio González Mendoza died (due to "liver disease", according to his death certificate). The entire city mourned his loss and dressed in mourning, all social and economic activities were paralyzed.

The School of Medicine took charge of the corpse and embalmed it between the 5th and 6th. The body mass was held on the 7th, in the Hospital chapel, on the cover of which the Medicine students placed a canvas, changing the title of Civil Hospital to "Hospital Gonzalitos". Later his remains were taken to the Government Palace, where official funeral honors were paid to him.

On April 8, the body of the worthy man was transferred to the “Gonzalitos Hospital” for burial. At four in the afternoon the cortege set off, led by the state and municipal authorities. Upon arrival at the Hospital, the coffin was placed in the portico, on a simple catafalque. In the background there were crepes and legends that accounted for the values of the wise doctor. On the right side of his remains, a gallery was improvised for the elegies and funeral prayers. At the conclusion of the ceremony, the coffin was taken to the interior chapel of the hospital, where the next day it was buried on the north wall.

A tombstone sculpted by F. Ferri with the inscription:

His memory will not perish and his name will be repeated from generation to generation. Ecclesiastical Chap. XXXIX, V.10.

Here lie the mortal remains of the Benemérito de Nuevo León. Dr. José Eleuterio González who knew how to live and die as a good son of God. DEP Monterrey, April 4, 1888.

The Monterrey School of Medicine in memory of its founder.

In his will he left a legacy, with which the upper floor of the old Hospital and the annex building of the School of Medicine were built, completed in 1892.

Dr. González persists in memory not only for his scientific, educational and humanistic work, but also for his philanthropy that led him to be loved and recognized by thousands of patients who received his care effectively and disinterestedly, they were the that from the youth of the wise doctor they immortalized him with the nickname of “Gonzalitos”.