For example, if nothing is connected to the OSC terminal of the J2120A and 5V is applied to the power supply terminal only, it works like a 3.5V output on the output terminal side.
Apparently, there is a fixed drop of about 1.5V from the input terminal to the output.
So, for example, when I want to apply 0.5V DC, the output side becomes 0V, and I'm having trouble with that.
Is this phenomenon a rare occurrence?
Could you also tell me what, if any, possible causes are and what measures you can take?
This is correct. See the web page and datasheet which show the voltage drop vs operating current. Also see the remote sense app note and PSRR solution page.
Picotest is currently offering a free J2120A remote sense PCB (see below image/Remote sense filter schem and BOM.pdf) if customer pays shipping. Contact info@picotest.com or emma@picotest.com for more details.