We have discovered seven type Ia cluster supernovae (SNe) in the course of the Wise Observatory Optical Transients Search in the fields of galaxy clusters with redshifts between z=0.06 and z=0.2. Two of these events, SN 1998fc in Abell 403 (z=0.10) and SN 2001al in Abell 2122/4 (z = 0.066), have no obvious hosts. Both events appear projected on the halos of the central cD galaxies, but have velocity offsets of 750-2000 km/s relative to those galaxies, suggesting they are not bound to them. We use deep Keck imaging of the locations of the two SNe to put upper limits on the luminosities of possible dwarf hosts, M_R > -14 mag for SN 1998fc and M_R > -11.8 mag for SN 2001al. The fractions of the cluster luminosities in dwarf galaxies fainter than our limits are less than 3 x 10^-3 and 3 x 10^-4, respectively. Thus, 2/7 of the SNe would be associated with less than 3 x 10^-3 of the luminosity attributed to galaxies. We argue, instead, that the progenitors of both events were probably members of a diffuse population of intergalactic stars, recently detected in local clusters via planetary nebulae and red giants. Considering the higher detectability of hostless SNe compared to normal SNe, we estimate that 20^{+12}_{-15} percent of the SN Ia parent stellar population in clusters is intergalactic. This fraction is consistent with other measurements of the intergalactic stellar population, and implies that the process that produces intergalactic stars (e.g., tidal disruption of cluster dwarfs) does not disrupt or enhance significantly the SN Ia formation mechanism. Hostless SNe are potentially powerful tracers of the formation of the intergalactic stellar population out to high redshift.

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