Given the emergence of deep learning, digital pathology has gained popularity for cancer diagnosis based on histology images. Deep weakly supervised object localization (WSOL) models can be trained to classify histology images according to cancer grade and identify regions of interest (ROIs) for interpretation, using inexpensive global image-class annotations. A WSOL model initially trained on some labeled source image data can be adapted using unlabeled target data in cases of significant domain shifts caused by variations in staining, scanners, and cancer type. In this paper, we focus on source-free (unsupervised) domain adaptation (SFDA), a challenging problem where a pre-trained source model is adapted to a new target domain without using any source domain data for privacy and efficiency reasons. SFDA of WSOL models raises several challenges in histology, most notably because they are not intended to adapt for both classification and localization tasks. In this paper, 4 state-of-the-art SFDA methods, each one representative of a main SFDA family, are compared for WSOL in terms of classification and localization accuracy. They are the SFDA-Distribution Estimation, Source HypOthesis Transfer, Cross-Domain Contrastive Learning, and Adaptively Domain Statistics Alignment. Experimental results on the challenging Glas (smaller, breast cancer) and Camelyon16 (larger, colon cancer) histology datasets indicate that these SFDA methods typically perform poorly for localization after adaptation when optimized for classification.