The Herschel Space telescope carried out an unprecedented survey of nearby stars for debris disks .
The dust present in these debris disks scatters and polarizes stellar light in the visible part of the spectrum .
We explore what can be learned with aperture polarimetry and detailed radiative transfer modelling about stellar systems with debris disks .
We present a polarimetric survey , with measurements from the literature , of candidate stars observed by DEBRIS and DUNES Herschel surveys .
We perform a statistical analysis of the polarimetric data with the detection of far-infrared excess by Herschel and Spitzer with a sample of 223 stars .
Monte Carlo simulations were performed to determine the effects of various model parameters on the polarization level and find the mass required for detection with current instruments .
Eighteen stars were detected with a polarization 0.01 \leq P \lesssim 0.1 per cent and \geq 3 \sigma _ { P } , but only two of them have a debris disk .
No statistically significant difference is found between the different groups of stars , with , without , and unknown status for far-infrared excess , and presence of polarization .
The simulations show that the integrated polarization is rather small , usually < 0.01 per cent for typical masses detected by their far-infrared excess for hot and most warm disks .
Masses observed in cold disks can produce polarization levels above 0.01 per cent since there is usually more dust in them than in closer disks .
We list five factors which can explain the observed low-polarization detection rate .
Observations with high-precision polarimeters should lead to additional constraints on models of unresolved debris disks .