I'd bet you are measuring a misleading "ghost voltage," which is a side effect of using a high-impedance voltmeter, which is the typical type of voltmeter, on a dead wire. This happens via capacitive coupling when you have an un-energized wire running next to an energized one and connect a high-impedance voltmeter. In your case, it would be from the switched wire running next to the hot wire.
To determine whether or not the voltage is actually present and being fed from a true voltage source, rather than being a misleading reading of an induced voltage from an adjacent wire, you need a low-impedance voltmeter.
What are ghost voltages and where are they encountered?
Ghost voltages occur from having energized circuits and non-energized
wiring located in close proximity to each other, such as in the same
conduit or raceway. This condition forms a capacitor and allows
capacitive coupling between the energized wiring and the adjacent
When you place your multimeter leads between the open circuit and the
neutral conductor, you effectively complete the circuit through the
input of the multimeter. The capacitance between the connected, hot
conductor and the floating conductor forms a voltage divider in
conjunction with the multimeter input impedance. The multimeter then
measures and displays the resulting voltage value.
Most digital multimeters available today have an input impedance
that's high enough to show the capacitively coupled voltage, giving a
false impression of a live conductor. The meter is actually measuring
voltage coupled into the disconnected conductor. However, these
voltages, at times, can be 80-85 % of what the "hard" voltage should
be. If not recognized as a ghost voltage, additional time, effort and
money will be lost troubleshooting circuit problems.
The most common places to encounter ghost voltages are blown fuses in
distribution panels, unused cable runs or electrical wiring in
existing conduit, open ground or neutral on a 120 V branch circuit or
in card cages where 120 V control circuits are used to control
assembly line or conveyor functions. Some amount of ghost voltage can
be coupled from the hot side to the open side across the blown fuse.
When facilities or buildings are built and wired, it's very common for
electricians to pull extra wire through the conduit for future use.
These wires are typically left unconnected until needed, but are
subject to capacitive coupling. In the case of the control circuits,
these circuits are typically located adjacent to unused control lines,
thereby creating a potential for a ghost voltage measurement.