If abusers are 4% of the system, if it costs more than 4% of the cost of all the benefits given, you actually waste money seeking abusers. Additionally, the abuse detection measures also have false positives, or long paperwork times, which filters out some legitimate users of the system.
This is a big issue with Social Security disability in the US, where things have to go through an abuse detection step, however this takes over a year almost in many states (SS Disability is oddly a per state run activity). By that time, the actually disabled have usually had their personal finances destroyed, or have worked in spite of severe danger to their health, both of which only up the end cost to the taxpayers.
An alternative (or even complementary measure) to strict abuse detection is graduated benefit reduction. (EDIT: By graduated benefit reduction, I mean, at the time you get a job, you do not lose all your benefits, you instead lose only a portion of them, say, 50%). That way moral hazard doesn't occur, as they get part of the benefit while working in a crappy job, thereby working is more attractive, but it still decreases the cost to the taxpayer, as highly qualified people may fill McJobs while looking for those in their real professions, and then not drawing the whole benefit.
We have a big issue with non-graduated benefits in the US, where it is the rational thing to do to accept benefits and not work with the incentive structure in some areas. If we change the incentive structure to promote work, overwhelmingly large number of current abusers would stop doing so and would take the work option.
Unemployment insurance in the US works for people who will make several times the unemployment amount when they get a new job. It's only the people who will make close to the dole amount after getting a job have issues with thinking it is a good alternative. As an economic rational actor, the people not taking the job may be making the correct choice with the unsophisticated system we have.
Graduated benefit reduction can work lots of places: Food stamps, section 8 subsidies, unemployment, social security, social security disability, re-education grants, etc.