Provided that you maintain power to the encoder and to the device that is counting pulses, it will act that way inherently. The problem only comes when you lose power. You could theoretically prevent movement with power off by adding some sort of brake to your moving equipment. You can put batteries on everything so that power can never go off. But in the end, I think you'll have to "home" the system at least every once in a while.
If power loss weren't an issue for you, or you reset to a home position independent of the encoder, you might be able to add additional circutry to add revolution count bits by
monitoring the encoder position.
Depending on what your application is, I have seen this done on a linear axis by adding a limit switch on the carriage, and at the point where the encoder crosses back over zero, the switch is turned on by a rail that travels the rest of the axis. In other words, the switch was off for the lower half of the run, and on for the second half. Some extra work was done in the logic since the mechanical switch couldn't be located exactly at the zero crossing. They ended up with a system where, for example, if the absolute encoder gave a value of 0 to 4096, they set the switch to come on anywhere over 4000. That way, if they had switch on and encoder value of 4050, they knew that it was the same as switch on and -46. Switch on and encoder value zero was the center of travel. Obviously, they lost 96 encoder positions at the extreme high end of the travel since they were used by the cross over logic. This was not an issue for this application, since they only used about 1/2 of the second rotation. It worked, though, and never needed homing.
Theoretically, this could be expanded to include multiple switches, although in practice, it might get pretty ugly....
You need other absolute device for counting of revolution number - for example the same other single-turn absolute encoder attached to the same shaft by gear. The gear ratio must be less than encoder's resolution.
