Like everyone else, I've no idea what a 'dry contact switch' means?
A common expression in the world of industrial controls is "Volt Free Contact", or sometimes "Volt and Earth Free Contact".
These expressions are used to describe a simple contact, either a switch or a relay contact, which is isolated from any electrical supply and earth.
The expression "Dry Circuit" is sometimes used where the voltage and current is so low that it cannot break through the oxide (?) layer on the surface of a relay contact.
An example of this was found in the amateur radio transceiver type FT102 by Yaesu.
In the RF circuits of the receiver section, there are many bandpass filters switched by relays.
These relays are switching signals at the microvolt level.
Over the years the contacts tarnish and the sensitivity of the receiver is severely impaired.
Part of the fix for this problem was to add resistors to give a "wetting current" to the contacts to prevent the problem recurring.
Coming back to the topic of the thread, the circuit described by the OP, sounds far from being a" dry contact".
It sounds like something which is intended to be connected to a Volt Free Contact.
JimB