A calculation can be a stored, indexed field. These are the default settings as long as the calculation does not reference an unstored, global or external (from another table/record) field.
One simple method, if you want to "hardwire" your value list to this one value in status is to add a calculation field to your table defined as:
If ( Status = "Client" ; FullNameCalc )
Then base your value list on the names returned by this field.
I do see another potential problem with your use of this value list, however. You should consider adding a serial number field to this table so that each record recieves a unique serial number value. Then set up your value list to refer to the serial number field in field 1 and this new calculation field for Field 2.
People's names are not unique and are subject to change. Linking records by an ID number avoids problems in both those cases.
Another way to create the value list you wish is to create a table with single field and record. this table would be for example Name_VL_Filter. and the field would be Status.
You would create a single entry of Client
then form a relationship between your Names table's status field and this new tables field.
In this way your are going to use a "conditional" value list
Then when you setup your value list select the option to show only related values from Name_VL_Filter