Thats already stated above.
take a £5k pay out and the car goes off to copart.
Take a £3k payout and keep the car, basically the insurance company are selling the car to the OP for £2000 which is a huge mark up on what its worth in that condition.
If the car has great sentimental value then it "might" be worth it. Only the OP can answer that.
@miaaa I would first go back to the insurance co and argue that the price of £5000 is too low. If it was previously a good condition car, the mileage is actually quite low, I would argue that its going to cost you £6000 to replace that car like for like.
They are low balling you on the value and thats very common with insurance companies. So firstly argue and settle on the value of the car before you decide if you want/intend to buy it back.
Then start arguing about the buy back cost, if you want to keep it.
The car is extensively damaged, it will need to go to a body shop to have the chassis leg straightened if that is damaged and that will be expensive. the whole front end will basically need to be stripped down its a lot of work, it needs specialist equipment.
It is going to need,
Bumper cover
bumper bar,
Headlight
DRL
Foglight,
Front wing
Driver's door.
Possibly bonnet, bonnet hinges,
Airbags? any deployed. airbag light on ?
That is a lot of money's worth of parts even second hand, and if you don't have the time, skills or inclination to do a lot of the work yourself you are paying the body shop, its going to come to more than £2k.
This is a list of all the 2015 Fiat 500's currently at Copart (the auction house that insurance companies use to sell damaged cars.) there are a lot of them right now so that tanks the value.
Here is a reason I would not buy this car back at £2000.
This is a Cat S which clearly doesn't have anywhere near as much damage
https://www.copart.co.uk/lot/500113...0-1-2-lounge-3dr-dualogic-start-stop-sandtoft
This hasn't met its reserve (at time of writing) at £1700. and bearing in mind it could take a lot less work to get that back on the road than yours. Thats "primary Damage dents and scratches" so likely repaired and then written off again with some minor damage but the Cat S marker was already on the car.
This is a Cat N which again at the time of writing was struggling to meet reserve at £1500
Here is a Fiat 500s 2015 on ebay that is hovering around the £1000 mark with much less damage than yours.
So £5000 is not enough to replace your car, argue for more with the insurance co.
£2000 buy back is too much. By the time they have paid to ship it to copart, storage fees and auction fees even if it made £2000 at auction which it definitely won't the insurance co would only be looking at getting a £1000 - £1500 back, and just to reiterate, it won't get £2k at auction so they won't get that much back, they will be lucky to break £1000 if they sell it at auction, or maybe far less if it does several rounds on the auction block.
Finally you need to decide how much sentimental value it holds because getting this repaired if you are not doing any of the work yourself and paying a bodyshop. It is definately going to be more than the car is worth, bearing in mind that it will now always be a CAT-S and will be worth less as a result.
Finally if your daughter is driving it about are you happy for your daughter to be driving a car you know has already had a heavy accident and needed repair work to essential crumple zones (the bent chassis leg).
Honestly I would encourage you to let it go. Do argue for more money from the insurance co, because it is low milage and was in likely very good condition before the accident.