Elias and Silver have supposedly known one another for quite some time. It's implied that Silver was introduced to Elias after he takes up ownership of the house, previously owned by a Victorian family (potentially Georgian, as the house is Georgian in design, but Silky's outfit is Victorian in nature suggesting the former). Not much is known about their relationship, other than the fact that Elias regards her as a landlady and respects her greatly. She does not seem to hold any disdain for Elias like the other neighbors do due to his nature as a "half-neighbor" being.
Silver appears to be quite attached to Chise, often doting on her. This is likely due to Chise's condition as a Sleigh Beggy. Silver appears to take great pleasure in serving Chise. When Chise collapsed for two weeks, Silver grew so worried that she tried to leave the house on her own to bring food to her. She is not above getting upset at Chise, such as when she and Elias forgot to finish breakfast due to being distracted by magic tools that Angelica sent to them.
Although their relationship seems somewhat one-sided, it appears that Chise has a friendly relationship with the Silver Lady. Chise remembered to buy souvenirs for her when she visited London while Elias was recuperating from the battle against Cartaphilus.
Silver Lady and Ruth have a odd, and largely unexplored relationship. In one of the omake's, Silver Lady is seen giving Ruth a bath (while he is in dog form), and is shown stating that Chise doesn't take enough care of him. A little after Christmas, when Chise and Elias are having a spat, Silver Lady fondles the underside of Ruth's jaw and the top of his head before giving him a pleasent wave when he goes to find Chise. Ruth, for his part, finds her behavior rather strange.
Spriggan stumbled upon Silver when she was wandering the lands as a Banshee. He is the one responsible for introducing her to Elias' home and turning her into a Silky. According to him, Silver is still considered to be a child. He considers it his duty to look out for lost neighbors like Silver and give them his protection. Silver is shown to be very grateful to him for giving her a new purpose in life and the two remain in contact.