Step 1: Recall what apoptosis is.
Apoptosis is programmed cell death. The cell actively shrinks, its chromatin condenses, the membrane blebs, and the cell finally breaks up into small membrane bound apoptotic bodies. The whole process needs energy and runs under tight control.
Step 2: Focus on the membrane.
Through this entire process the plasma membrane stays intact until the very end. Because the cell contents are never spilled into the surrounding tissue, there is nothing there to trigger an inflammatory response. This is the single biggest difference from necrosis, where the membrane ruptures early and cell contents leak out, calling in neutrophils and causing inflammation.
Step 3: Check the remaining statements one by one.
Macrophages do take up the apoptotic bodies through phagocytosis, and they do this quietly, without releasing pro-inflammatory signals, so this statement is true of apoptosis. Caspases, a family of cysteine aspartate proteases, are indeed the enzymes that execute the death program, cutting structural and regulatory proteins, so this is also true. Endonucleases are activated during apoptosis and cut nuclear DNA at regular intervals between nucleosomes, causing the chromatin to condense and fragment, a process called chromatolysis, so this statement is true as well.
Step 4: Final answer.
Since apoptosis is specifically defined by the absence of an inflammatory reaction, the statement that is NOT true is
\[ \boxed{\text{Surrounding inflammation}} \]