Recent progress in active-edge technology of silicon sensors enables the development of large-area tiled silicon pixel detectors with small dead space between modules by utilizing edgeless sensors. Such technology has been proven in successful productions of ATLAS and Medipix-based silicon pixel sensors by a few foundries. However, the drawbacks of edgeless sensors are poor radiation hardness for ionizing radiation and non-uniform charge collection by edge pixels. In this work, the radiation hardness of edgeless sensors with different polarities has been investigated using Synopsys TCAD with X-ray radiation-damage parameters implemented. Results show that if no conventional guard ring is present, none of the current designs are able to achieve a high breakdown voltage (typically < 30 V) after irradiation to a dose of ∼ 10 MGy. In addition, a charge-collection model has been developed and was used to calculate the charges collected by the edge pixels of edgeless sensors when illuminated with X-rays. The model takes into account the electric field distribution inside the pixel sensor, the absorption of X-rays, drift and diffusion of electrons and holes, charge sharing effects, and threshold settings in ASICs. It is found that the non-uniform charge collection of edge pixels is caused by the strong bending of the electric field and the non-uniformity depends on bias voltage, sensor thickness and distance from active edge to the last pixel (``edge space"). In particular, the last few pixels close to the active edge of the sensor are not sensitive to low-energy X-rays ( < 10 keV), especially for sensors with thicker Si and smaller edge space. The results from the model calculation have been compared to measurements and good agreement was obtained. The model can be used to optimize the edge design. From the edge optimization, it is found that in order to guarantee the sensitivity of the last few pixels to low-energy X-rays, the edge space should be kept at least 50% of the sensor thickness.