After Linda (Harriet Jacobs) escapes, the Flints are desperate to find her and bring her back. Linda even notes that the Flints are afraid of her fleeing before she even does so:
Mr. Flint was hard pushed for house servants, and rather than lose me he had restrained his malice. I did my work faithfully, though not, of course, with a willing mind. They were evidently afraid I should leave them. Mr. Flint wished that I should sleep in the great house instead of the servants' quarters. (ch. 17)
Linda senses that Mr. Flint makes her a house servant to ensure she stays on the plantation. However, Linda decides to escape anyway. We see that she does not serve as a house slave "with a willing mind." She is still bent on escaping slavery.
After the Flints realize Linda is gone, they start by "inquiring for [her]" at her grandmother's house. This is the obvious place she would go to for shelter, but of course, Linda knew they'd look for her there, so she did not actually hide at her grandmother's house until later. They also question her grandmother but are relieved to find that the children remain. Flint thinks that means Linda isn't far away or might come back. Nonetheless, they search the entire house before moving on.
Dr. Flint also tries to offer a reward for Linda's return. This was common practice in the antebellum South: when a slave escaped, plantation owners attempted to persuade the public to help by giving them money. The "advertisement was posted at every corner, and in every public place for miles round:—" and offered the person who would return Linda to the Flints a $300 reward.
For a long time after, we see Jacobs describing the difficult conditions Linda has to endure to "hide in plain sight." She is able to remain hidden but she's in a constant state of danger and is always alert to the possibility that she could be caught. She sees Flint from her hiding space, as he continues a seemingly endless search for her.