'Suffering' in Buddhism means the pain we create for ourselves, not pain which is outside our control. Buddhism won't stop others assaulting you, stop you having accidents or stop you getting sick.
The suffering we create for ourselves, according to Buddhism is not spontaneous, in the sense of arising by itself, but has a cause, which is our ignorance.
"Monks, an uninstructed run-of-the-mill person feels feelings of
pleasure, feelings of pain, feelings of neither-pleasure-nor-pain. A
well-instructed disciple of the noble ones also feels feelings of
pleasure, feelings of pain, feelings of neither-pleasure-nor-pain. So
what difference, what distinction, what distinguishing factor is there
between the well-instructed disciple of the noble ones and the
uninstructed run-of-the-mill person?"
"For us, lord, the teachings have the Blessed One as their root, their
guide, & their arbitrator. It would be good if the Blessed One himself
would explicate the meaning of this statement. Having heard it from
the Blessed One, the monks will remember it."
"In that case, monks, listen & pay close attention. I will speak."
"As you say, lord," the monks responded.
The Blessed One said, "When touched with a feeling of pain, the
uninstructed run-of-the-mill person sorrows, grieves, & laments, beats
his breast, becomes distraught. So he feels two pains, physical &
mental. Just as if they were to shoot a man with an arrow and, right
afterward, were to shoot him with another one, so that he would feel
the pains of two arrows; in the same way, when touched with a feeling
of pain, the uninstructed run-of-the-mill person sorrows, grieves, &
laments, beats his breast, becomes distraught. So he feels two pains,
physical & mental.
http://www.accesstoinsight.org/tipitaka/sn/sn36/sn36.006.than.html