You can find out a property using .GetTOProperty() I have not used them for a while but you can make a change to a property during run time. Also you can save the OR during run time. I don't remember how to do this part.
In the Object Repository you can add or remove which properties QTP uses to recognize the object. If you are using descriptive programming, QTP will use only the properties that you put inside the desctiption to recognize the object.
Why do you want to do this? The "value" property is the currently selected value in the WebList. The "all items" property is a semi-colon separated list of all the possible values from the WebList field. It doesn't make sense to set the property "value" (which is one item from the list) to a string representing all the values in the list.
Additionally, if you are talking about the objects in the Test Object Repository, the properties noted there are for identification purposes. They are used during the run of the test to try to identify the object in the UI. The default mandatory properties for a WebList are "name" and "html tag". Are you using "value" as another mandatory property, or an assistive property? Why do you want to modify the value of property in your Test Object Repository? Or are you really trying to modify the value on in the Runtime Object Repository?
If you explain what you are ultimately trying to accomplish, perhaps we will be able to provide more meaningful answers.
The weblist you are referring shouldn't have any default value selected that is when you add/spy the object default value shows to empty.
Try the following scenario
Spy the 'WebList' and check what is coming as value(It should be empty)
Select one value from the WebList and Spy now then check what is coming as value(It should be the value what you selected in dropdrown)