What should I put on my almost empty PCB layer?
What is typically done in the industry in these cases, assuming that ground-fill practices as shown in other answers does not provide significant benefit, is something called thieving.

Thieving consists of covering large expanses of unused outer layers with a pattern of shapes, usually diamonds or squares, disconnected from one another. Thse shapes are kept away from other features, such as holes, board edges, or traces. The sole purpose of thieving is to improve manufacturability by ensuring a constant PCB thickness given any particular area on the board, say, half a square inch.

Without thieving, the rollers that are used to laminate the layers together will not exert as much force on the copper-starved areas, which could lead to delamination (looks like light spots inside the board).