If we consider the theory of a single relativistic point particle, quantized using whatever appropriate method, the wavefunction simply obeys the Klein-Gordon equation, which allows for a fairly wide range of initial solutions, including solutions of compact support.
In which case, we can consider the proposition of the presence of the particle in some region of space $\Delta$, noted by $P_\Delta$ :
$$P_\Delta (\psi) = \int_\Delta d^3x\ \frac i2 [\psi^* (\partial_t \psi) - (\partial_t \psi^*) \psi]$$
If we pick a wavefunction of compact support, this propositon should be equal to $1$ in the support of the wavefunction, as $\psi$ will be $0$ outside of it and the probability should add up to unity.
However, according to Malament's theorem, a reasonable relativistic quantum theory with the possibility to localize particles in this manner should have, for any compact $\Delta$, no possibility for the probability to add up to $1$ in this region. In other words there should be no finite region in which the particle should be measured with certainty.
Where is the problem here? Does the measurement for such a compact support wavefunction somewhat cancel out? Does this system not fulfill the requirements of the theorem, or am I misunderstanding the content of Malament's theorem?
Also in the case of Klein Gordon for QFT, while describing the localization of a field is less straightforward, it would seem that a wavefunction where the measurement of the field $\hat \phi |\Psi \rangle$ is of compact support might also fulfill the same requirements, is there also a problem there?