Last time I checked a cheap car in Singapore was in the region of $100k USD.
You're talking about low end Japanese and below. The price varies due to the need to bid for permits, but I don't think you can get a new Mini or Volkswagen for only 100k USD.
And as for that stuff about leaving your car running in the street - well, all Singapore cars are fitted with special devices that record when you pass traffic gantries, and most traffic junctions have cameras. A thief can't really go anywhere with a stolen car. Not to mention, garages and parking spaces are all either public, or else located inside multimillion dollar homes. The price for a teeny weeny leasehold apartment is around 800kUSD and the price for a cheap landed house with garage is minimum 1.5m USD.
There is no way a thief can find a private place to mod a stolen car. It's one of the least likely things to get stolen in Singapore. Elrick, if you wore a t-shirt with your national animal on it and hung around outside Singapore's courts, you'll probably get arrested, charged in court, after which you won't like Singapore anymore. Already three people have been jailed for no other reason than wearing t-shirts with Kangaroos on them outside a courthouse.
Yup, that's what it means to live in a Disneyland owned by the Wizard of Oz. We're just downtrodden Munchkins ruled by false characters with no courage, no brains and no hearts.