Short answer. No, not if that country denies reciprocity. Rule 88 lets foreign-proven claims share in a Philippine estate, but withdraws that benefit from creditors in a country whose own property is not equally apportioned between Philippine-resident creditors and its own, according to their respective claims — reciprocity is required.
What the law says
but the benefit of this and the preceding sections shall not be extended to the creditors in another country if the property of such deceased person there found is not equally apportioned to the creditors residing in the Philippines and the other creditors, according to their respective claims.
Rule 88, Section 10 — When and how claim proved outside the Philippines against insolvent resident's estate paid. Read the full provision →
How a foreign claim normally gets added to the estate here
Rule 88, Section 10 lets a court include a debt proven abroad in the local distribution: the court shall receive a certified list of such claims, when perfected in such country, and add the same to the list of claims proved against the deceased person in the Philippines so that a just distribution of the whole estate may be made equally among all its creditors according to their respective claims. That is the general benefit — pooling foreign-proven claims with local ones for a fair, combined distribution.
Two conditions attach before that benefit is available
The rule only reaches this stage when claims have been duly proven in another country against the estate of an insolvent who was at the time of his death an inhabitant of the Philippines, and that the executor or administrator in the Philippines had knowledge of the presentation of such claims in such country and an opportunity to contest their allowance. Both the decedent's Philippine residency and the local administrator's fair chance to contest the foreign claims have to be satisfied.
The reciprocity condition that removes the benefit
Rule 88 then withdraws the benefit in the exact situation you describe: the benefit of this and the preceding sections shall not be extended to the creditors in another country if the property of such deceased person there found is not equally apportioned to the creditors residing in the Philippines and the other creditors, according to their respective claims. If that foreign country's own distribution process does not give Philippine-resident creditors an equal share of the property found there, creditors from that country lose the right to share in the estate administered here.
What this means for your relative's estate
Applying this directly: whether creditors from that other country may still share in your relative's Philippine estate turns on whether that country apportions property equally between its own creditors and Philippine-resident creditors. If it does not, Rule 88 itself removes their access to the pooled distribution described above, and the estate administered here would be distributed among the local and duly proven claims without regard to that country's unrecognized creditors.