Why is this resistor only connected on one side?
Perhaps you can provide more information on the board. Are there no connections or components on the other side of the board?
There is usually no 'use' for an unconnected resistor.
Otherwise this is likely done for manufacturing or testing reasons.
Perhaps the resistor is used for probing a certain setting or the board exists in multiple configurations where for instance an option is 'installed' or changed by connecting a jumper (0 ohm resistor) or another component between the close pads that are also visible.
To get the real reason you must ask the manufacturer :-)