The ending of "The Son's Veto" is veiled in suggestion on purpose to give the reader a moment of mild horror at the reality of Sophy's situation and of Randolph's inner traits. The resolution is thus intentionally elusive (though not ambiguous); Hardy would be pleased that his technique of suggestion succeeded and readers must do a double-take and reread the last passage to truly understand what has happened. Let's piece the resolution together.
Randolph has made his mother swear before an alter in his room that she will never "wed Samuel Hobson without his consent." Hardy subtly implies that many years go by with the line, "Her lameness became more confirmed as time went on." He also implies that the stress and sorrow of forestalled happiness is wearing her down because she "would murmur plaintively to herself when nobody was near," saying "Why mayn't I say to Sam that I'll marry him? Why mayn't I?"
Next, Hardy switches his point of view to "a middle-aged man [who] was standing at the door of ... a fruitier shop" in a neat suit of black." Here, the reader doesn't actually know who is spoken of--as Hardy intends--but suspects it must be Sam. We hope, despite the change in narrator tone, that he is wearing black in front of a "partly shuttered" window because it is his wedding day and Sophy has finally defied her son's veto and will marry Sam.
Then Hardy throws us into confusion by telling that a "funeral procession was seen approaching." What does the funeral mean to Sophy and Sam? Whose funeral is it? That the man's "eyes were wet" as the funeral past by contradicts our hope of a marriage between Sam and Sophy--if indeed the man is Sam--still we are not sure of what is being presented.
Then we learn who is riding on the mourning coach. It is a newly ordained clergyman: "a young smooth-shaven priest." He looks "black as a cloud." His black look is aimed directly at the man with wet eyes in a black suit with his hat in his hands. Then we know--against our wills we realize--the man standing thus in front of his shuttered shop is Sophy's own Sam. The cold and hard "priest" with the high collared "waistcoat" is Randolph, from whom his "education had ... ousted his humanity." The one riding at rest in the funeral carriage is lame Sophy who has died under Randolph's crippling veto. It is Sophy, Randolph's mother and Sam's love, who has died.
The ending was Sophy's funeral, and the bald priest is her son randolph
Basically, Sophy passed away and she never got her consent from Randolph to marry Sam. And Sam's become the best fruitseller in town. And Randolph is attending the funeral and he's become a priest.
It's Sophy's funeral. Sam Hobson is dressed in a Black Suit as a sign of mourning. Randolph is the Priest. And Sam Hobson had left his job just to attend Sophy's funeral so that he may once again remember the good old moments he spent with Sophy. Hardy depicts the image of Grief and sorrow in a very sublime way.
In the end of story it is revealed that pressure of the society and the ignorance of his son and husband speeds her to grave.