What makes chainsaw leak bar oil when not in use?

Two possible causes, the fill plug is not sealing or the oil is syphoning through the line that oils the chain.

Check the plug, it may have a thin sealing washer or 'O' ring that has become damaged or is missing. If it was designed not to have a separate seal then the plug threads or sealing seat may be damaged or packed with dirt. Replace or clean.

If the oil seems to be running out via the delivery line to the bar the tank vent is plugged, if this is the case the chain will probably be running 'dry' during operation.

The vent may be in the plug, would be crossed drilled so the hole is up when the saw is setting in the normal position. If in the case it would likely be concealed by the starter cover. It may be covered with a small mesh. You can clean blocked plugs with a suitable size piece of wire/and or aerosol spray WD40, etc. with the small delivery tube. Case vents vary but the aerosol method should clean most types.