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Under normal circumstances the cell wall will prevent too much water from entering. When the wall is weakened through the use of enzymes or freezing. The cut flowers get weak because the cells dry out and lose their turgorr which was keeping it upright. This lack of water also kills the plant

The plant cell that burst (in the absence of / with severe degradation of the wall) would look roughly similar to an animal cell, albeit with possible chloroplasts in them