I want to get a used Toyota Prius Mk2 (XW20). I do not necessarily need to operate it in hybrid mode (gas + electric) and I am OK with operating it in a kind of "gasoline only" mode (because of a research project). My main concern is the traction battery wear - a used Prius is likely to have a worn out battery and I may not be wanting by replacing it with a new one. Can I operate the car with a worn-out main traction battery? Will the car's electronics switch to "gasoline only" operation mode or how will it work?
This is in theory possible, but I have no idea how to implement it in practice.
The Prius HSD "Hybrid Synergy Drive" has, at its transmission heart, a planetary gearset with two power inputs: One from the internal combustion engine, and one from the AC motor/alternator. Each acts on a different element of the planetary set (carrier, ring, I don't recall which is which) to create what Toyota calls e-CVT or electronic continuously variable transmission. Any combination of electric motor or ICE power is possible, including regenerative breaking, using the traction motor as a starter, and ICE to traction motor/alternator recharging of the battery package.
The problem is that a sophisticated "ECU" or maybe better described in the case of a hybrid as a Powertrain Control Module controls every last detail of this complex dynamic power flow. The Prius, along with other Toyota HSD vehicles, is completely "fly by wire" with no physical driver input to any drivetrain system. All functions are merely software requests to the drivetrain computer.
So, it's possible that a Prius with a dead battery will default to an ICE-only mode. But to force this condition would require very complex ECU programming. And honestly, I don't think you can even start the vehicle if the battery is dead.
Further, I'd think that a used Prius with a dead or "worn out" battery would be quite obvious and avoidable before purchase.
No, it is not possible
At least not without some mechanical modifications. This diagram shows how the Power Split device works. The Prius has two electric engines , Motor Generator 1 (MG2) and Motor Generator 2 (MG2), and one Internal Combustion Engine (ICE), linked by the Power Split Device (PSD). The MG2 is locked to the wheels (no clutch or torque converter in-between) and the rotation of the ICE and MG1 is a function of each other, respectively, and the MG2.
If you have no electric power, the MG1 and MG2 will turn loose. The problem is that the MG1 offers no resistance to turn while the MG2 would be tied to the wheels, thus remaining stopped.
Think like a car with one wheel stuck in mud and the other in firm ground. The wheel with less resistance (the one in the mud) will turn loose while the one in firm ground will offer resistance because the differential does not "know" that it "should" move the more firm wheel, not the loose one, unless you have a differential lock or other device that distributes the power "fairly".
The solution for this would be locking the MG1, so the ICE would turn the MG2 instead, which would be offering less resistance, on this case.
If the battery pack is completely worn out, you cannot use the Prius in a gasoline-only mode, because the high voltage battery pack is the only way the internal combustion engine can be started. There is no 12V starter motor in the Prius. If there is some juice and lifetime left in the battery, it can start the internal combustion engine, meaning that motor-generator 1 (MG1) can supply the power MG2 needs or vice versa. So, after startup, Prius is generating the electricity it needs. Some lifetime left in the battery is probably necessary for buffering the high-voltage electrical system.
However, if the battery pack is only somewhat worn out, it just means the electric-only range which is already short (1-2km) will be even shorter, perhaps hurting fuel economy. This is not in any way a problem, as the battery is oversized for the job it does, see my answer to Is there a diagnostic that can be done on a used hybrid car's battery pack? for the detailed calculations.
Consumer Reports has tested an old Prius with 200 000 miles, and the mileage was the same as when new. Also, many Priuses (Prii?) are used in taxicabs, and they work in this severe application quite well. So, you probably don't have to worry about the Prius battery. I understand that Honda hybrids have had battery troubles, but no such trouble is there for Toyota hybrids. Also, in Finland, there is a 10 years / 350 000 km warranty for the hybrid battery. If the battery really wears out, chances are that a $500 junkyard battery will have much lifetime left, as battery failure is so rare in these hybrids.