Cell cycle arrest and apoptosis
Apoptosis can occur without cell cycle already being arrested.  For instance, in the case of extrinsic apoptosis, which could be induced by T lymphocytes, for example, a trimeric receptor such as TNF-R or TRAIL-R's containing a DD can be bound at any time by the death ligand secreted by (TNF, TRAIL) or bound to the immune cell membrane (FasL, TRAIL).
The DD (death domain), independent of where cell cycle is, recruits adaptor proteins with DED domains (ie., FADD), which in turn recruit procaspase 8.  Procaspase 8 is cross-activated (becoming caspase 8) when two of them are recruited, then released.  It then begins activating procaspases 3, which begins the actual work of killing the cell (cutting cytoskeleton =&gt; blebbing, etc.), activating CAD.
It bears mentioning, however, that once it's kicked in, cell cycle will inevitably stop, since CAD will start fragmenting the DNA...  It also bears mentioning that caspase 8 also activates the intrinsic pathway via Bid =&gt; tBid =&gt; Bax =&gt; Bak =&gt; mitochondrial leakage, cytochrome C activating caspase 9...

Sources:

Sayers, Thomas J. 2011. Targeting the extrinsic apoptosis signaling pathway for cancer therapy. Cancer Immunology, Immunotherapy 60 (8): 1173-80.

Eimon, P. M., E. Kratz, E. Varfolomeev, S. G. Hymowitz, H. Stern, J. Zha, and A. Ashkenazi. 2006. Delineation of the cell-extrinsic apoptosis pathway in the zebrafish. Cell Death and Differentiation 13 (10): 1619-30.