You have linked to another discussion which contains a broken link to the product you say you have. Sort of unhelpful.
If the relay module you are using, which you could have provided a link for, has a normally closed relay on it, and it's hard to tell with the extreme lack of specificity here, you are screwed. When it is off, the relay is closed, end of story. Get a different module.
I hope that is not the case. It sounds like when there is no input to the relay module the input is floating and somehow floats to a signal level where the relay module closes the relay without there being any signal. If this is the case, the normal solution is a pull up or pull down resistor, whichever causes the module to leave the relay open. Approximately any higher value resistor will do, probably try a 4.7K or 10K one and if for some reason that isn't strong enough, use a 1K.