Did they vote in favour of any of the proposals recently made in Parliament?
In the first round of indicative motions the DUP voted for the "standstill transition" motion and abstained on a couple of others.
The motion labelled "standstill transition" here must mean Option O - "Contingent preferential arrangements" proposed by Mr Marcus Fysh and defeated by 422 to 139
The full text of that motion includes
That this House directs that in case the UK is unable to implement a Withdrawal Agreement with the EU, Her Majesty’s Government shall seek to agree immediately and preferentially with the EU:
(a) a trade agreement ...
(b) a standstill period of mutual recognition of standards and conformity assessment for up to two years in which the UK will ensure compliance in the UK with the EU legislative acquis as adopted in Retained EU law under the EU Withdrawal Act on the day the UK leaves the EU notwithstanding that these arrangements may be superseded or extended by further mutual agreement;
(c) a customs arrangement ... and
(d) make provision for the payment of sums to the European Union ...
(I have elided text for brevity)